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A co-jump network approach to systemic risk measurement: Evidence from the U.S. financial market - ScienceDirect
Economic Modelling
Volume 158, May 2026, 107534
A co-jump network approach to systemic risk measurement:
Evidence from the U.S. financial market ☆
Shijia Song a
, Handong Li b
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https://doi.org/10.1016/j.econmod.2026.107534
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Highlights
•
A co-jump network framework to measure systemic financial risk is
developed.
•
Co-jump connectedness captures both left- and right-tail dependencies
using public data.
•
Empirical results reveal structural shifts in U.S. systemic risk after
COVID-19.
•
The framework outperforms MES and CoVaR network in
macroprudential risk management.
•
The proposed measure also supports portfolio-strategy optimization.
Abstract
This study proposes a co-jump network framework for measuring systemic risk by more accurately capturing latent
interconnectedness among financial institutions. To address key limitations of traditional network connectedness measures,
namely reliance on nonpublic data, a focus on one-sided tail dependence, and insensitivity to discontinuous shocks, we estimate
a Tobit-LASSO model to identify significant co-jump dependence after controlling for macro common factors and institutionlevel characteristics. We then establish the co-jump network and define a realized systemic jump beta as the risk metric.
Empirical results based on U.S. financial data show that the proposed method outperforms benchmark models, including the
CoVaR network approach and MES (DCC-GARCH based), in capturing the structural shift in systemic risk during the post-COVID
period, when the persistent effects of the pandemic shock were not fully offset by the short-term market rebound. The analysis
also highlights liquidity providers and highly leveraged intermediaries as primary contributors to systemic risk, while insurers
are comparatively underrepresented. Furthermore, a mean–variance strategy augmented with our systemic risk measure is
shown to help avoid extreme downside losses. Overall, the co-jump network offers a theoretically grounded and empirically
practical tool for risk management that benefits both regulators and investors.
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G10
Keywords
Co-jump; Systemic risk; Financial network; Tobit-LASSO; Tail dependence
1. Introduction
The global financial crisis underscored the severe impact of systemic financial risk on financial stability, macroeconomic
performance, and social welfare, prompting governments and regulatory bodies to prioritize its monitoring and prevention.
However, a unified measurement framework for systemic risk remains elusive, posing ongoing challenges for both academia and
practice (Freixas et al., 2015). Existing methodologies generally fall into three broad categories. The first involves constructing
composite indices using early warning indicators and statistical techniques, such as the Financial Stress Index (FSI) (Illing and Liu,
2006, Oet et al., 2015) and the Composite Indicator of Systemic Stress (CISS) (Hollo et al., 2012). While intuitive, these approaches
may be vulnerable to subjectivity in indicator selection and weighting. The second focuses on estimating potential losses under
tail events to evaluate institutions’ systemic exposure or contribution, as seen in measures like
CoVaR, MES, SRISK and CATFIN
(Adrian and Brunnermeier, 2016, Acharya et al., 2017, Brownlees and Engle, 2017, Allen et al., 2012). These approaches, however,
often overlook the complex interconnections among institutions. The third adopts a network-based perspective to capture risk
spillovers and interconnectedness within the financial system through structural metrics (Baruník and Křehlík, 2018, Diebold and
Yılmaz, 2014, Härdle et al., 2016, Xu et al., 2019), offering a more holistic view of systemic importance. The 2008 crisis marked a
turning point, revealing that network interlinkages among financial institutions can significantly amplify systemic risk. This
realization shifted the regulatory focus from microprudential to macroprudential oversight and from “too big to fail” to “too
interconnected to fail”. In the post-crisis era, precisely capturing the structural relationships among financial institutions has
become critical for both improving risk measurement and deepening our understanding of systemic risk. Building on this
perspective, we aim to propose a novel network-based modeling framework that quantifies financial interconnectedness and
develops corresponding measures of systemic risk, contributing both theoretically and practically to risk monitoring.
Although systemic financial risk is a widely used concept, there is no consensus on a precise definition. Supervisory authorities
(e.g., ECB, IMF, BIS, FSB) tend to adopt a macro perspective, viewing it as the risk that financial instability becomes sufficiently
widespread to damage parts or the whole of the financial system and, in turn, materially affect the real economy, social welfare,
and public confidence (Billio et al., 2012, Bisias et al., 2012). Academic definitions are typically grounded in specific mechanisms,
including crises triggered by abrupt breakdowns in the flow of information in financial markets (Mishkin, 2007), nonlinear
feedback and amplification of liquidity risk (Kapadia et al., 2012), and the accumulation and sudden collapse of asset price
bubbles (Brunnermeier et al., 2020). Despite these different emphases, the definitions converge on two core features of systemic
risk. First, externalities and contagion: shocks, dislocations, or losses affecting one institution or market can propagate rapidly to
others. Second, nonlinearity and suddenness: systemic risk does not arise from the linear aggregation of idiosyncratic risks but
instead can erupt abruptly from seemingly tranquil conditions. Constructing network connectivity measures that faithfully
capture these features is therefore a prerequisite for accurate measurement of systemic risk.
Existing measures of network-based financial risk connectivity can be broadly classified into two categories: exposure-driven
and market-driven approaches. The former relies on non-public data such as interbank credit exposures and primarily serves
regulatory purposes within a limited scope (Allen and Gale, 2000, Leitner, 2005, Freixas et al., 2000, Allen et al., 2009). In
contrast, the latter leverages publicly available market data, typically asset prices, to characterize linear or nonlinear
dependencies among institutional returns and volatilities. The work of Diebold and Yılmaz (2014) highlighted the importance of
the concept of “connectedness” in identifying systemic risk and proposed a network-based framework grounded in vector
autoregression (VAR) models to measure such connectedness among financial institutions. Their work gave rise to a range of
VAR-type connectedness indicators, including the Frequency Connectedness measure (Baruník and Křehlík, 2018), TVP-VAR
Connectedness (Antonakakis et al., 2020), and DCC-GARCH Connectedness (Gabauer, 2020). However, VAR-based methods
assume a linear dynamic structure and capture interdependencies through linear Granger causality. This assumption may fail to
reflect the nonlinear nature of risk spillovers, especially under extreme market conditions. As a result, these models may
underestimate systemic risk arising from tail events or complex nonlinear interactions. To address this limitation, recent studies
have focused on tail risk dependence among financial institutions and developed corresponding models under network
framework. Hautsch et al. (2015) utilized conditional Value-at-Risk (CoVaR) to measure tail risk and employed quantile
regression combined with LASSO to identify key tail risk drivers, thereby constructing a CoVaR network. Building on this, Härdle
et al. (2016) introduced the TENET (Tail-Event driven NETwork risk) model, which integrates quantile regression with a singleindex model to allow for nonlinear amplification of tail dependencies and better capture high-dimensional nonlinear
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interactions. Further, Chatziantoniou et al. (2021) extended the traditional VAR framework to the quantile domain by proposing
the Quantile VAR (QVAR) connectedness approach. This model characterizes the dynamic dependence structure of institutions
across different parts of the return distribution, making it possible to capture systemic risk spillovers under extreme market
conditions. Nonetheless, these tail-dependence-focused models also face limitations. First, they typically capture dependence at
a single quantile level—most often in the lower tail. However, upper-tail dependence often implies the presence of bubble risk.
Minsky famously argued that “stability is destabilizing”, highlighting that systemic fragility tends to accumulate beneath the
surface of apparent prosperity. Although upward trends in the stock market manifest as rising prices, they frequently signal the
build-up of systemic risk. Historical experience shows that many financial crises did not originate from negative shocks, but
rather from the sudden bursting of accumulated bubbles. For instance, events such as the 1987 “Black Monday”, the 2015 Chinese
stock market crash, the 2022 UK LDI debt crisis all occurred following sharp price increases and were marked by abrupt reversals.
Therefore, from a financial stability perspective, accurately capturing upper-tail dependence is equally crucial for identifying
systemic risk. Yet, conventional connectedness measures fail to simultaneously reflect the dependence structure of both tails of
the return distribution. Second, these models primarily focus on continuous extreme movements (e.g., prolonged price surges or
crashes), while overlooking discontinuous shocks such as defaults, flash crashes, or sudden local failures. Consequently, they may
underrepresent the role of such abrupt events in shaping tail dependence and contributing to systemic risk.
Motivated by this background, we focus on the salient phenomenon of jump contagion during crises: large and abrupt price
discontinuities in one asset or even a market index over short intervals can induce discontinuous moves in other assets or
markets, manifesting as widespread co-jumps (Gilder et al., 2014, Arouri et al., 2019, Semeyutin et al., 2021, Zhang et al., 2023,
Zhang et al., 2024). This is a direct manifestation of the externalities and nonlinearity that accompany the outbreak of systemic
risk (Das and Uppal, 2004). A widely accepted view attributes jump behavior to the arrival of major information shocks, such as
news announcements, policy changes, or macroeconomic surprises (Dungey et al., 2009, Baker et al., 2020). However, empirical
evidence suggests that only about one-third of large price movements can be linked to public information (Brogaard et al., 2022).
Many extreme price fluctuations stem from internal market dynamics or feedback mechanisms, and are often associated with
liquidity shocks (Ahn and Tsai, 2021, Lahaye et al., 2011). Therefore, co-jumps reflect synchronized risk fluctuations driven by
both exogenous and endogenous forces. They may originate from external systemic shocks, or from endogenous linkages such as
inter-firm credit relationships, business similarities, or industry-specific risk factors. This highlights the unique value of co-jumps
in revealing latent interconnections among financial institutions without relying on private data. Moreover, co-jumps have been
shown to enhance volatility comovement and tail dependence across assets (Wang et al., 2015, Caporin et al., 2017, Li et al., 2016,
Bollerslev et al., 2013, Yeh and Yun, 2023). In essence, they offer an observable manifestation of the complex dependences among
financial assets. Importantly, jumps are directional, as they indicate both positive (upside) or negative (downside) discontinuous
price movements. Hence, a network connectedness measure based on co-jumps can effectively capture bi-directional non-linear
dependencies, addressing key limitations of traditional connectedness metrics that often focus only on linear or one-sided tail
dependence.
Despite its potential, the integration of co-jump phenomena into network frameworks remains in its early stages. Ding et al.
(2024) proposed a co-jump network model in which nodes represent assets and edge weights correspond to co-jump
frequencies. Co-jumps are identified using a two-step procedure. First, jumps in individual assets are detected using classical
tests such as the BNS test (Barndorff-Nielsen and Shephard, 2006), ABD test (Andersen et al., 2007), L-M test (Lee and Mykland,
2008), S-BNS test (Andersen et al., 2010), or TOD test (Bollerslev et al., 2013). Then, a co-jump is recorded when jumps across
different assets occur simultaneously (Gilder et al., 2014). Although this co-jump network framework has been applied to
portfolio optimization in equity, cryptocurrency, and foreign exchange markets (Zhang et al., 2023, Zhang et al., 2024, Zou et al.,
2024), it exhibits substantial limitations in capturing the multifaceted interactions and systemic risk propagation among
financial institutions. These limitations can be summarized in four key aspects. First, traditional co-jump tests focus solely on the
temporal coincidence of jumps, neglecting their magnitudes. However, accounting for both timing and size can more accurately
reflect directional influences and mutual jump triggering across assets. Second, co-jump frequency is a scalar measure and lacks
directionality, resulting in a symmetric network that fails to distinguish between risk transmitters and recipients. Third, the
network is built exclusively on pairwise co-jump relations, ignoring indirect effects mediated through other institutions and
making it difficult to capture system-wide risk transmission pathways. Fourth, co-jumps identified purely by temporal overlap
may stem from common macroeconomic shocks or widespread credit deterioration, rather than institution-specific risk
channels. By contrast, co-jumps triggered by credit exposures, liquidity strains, or sector-specific shocks are more informative for
tracing targeted contagion mechanisms. For these reasons, the current co-jump network model has not yet been applied to
systemic risk measurement. There is an urgent need to develop an enhanced framework that better reflects underlying financial
interdependencies and enables the use of network topology for quantifying systemic risk, both at the institution level and for the
entire financial system.
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In summary, constructing network connectedness measures based on co-jumps offers a novel perspective for both theoretical
and applied research on systemic financial risk. However, two critical challenges remain: how to quantify co-jump-based
dependencies among financial institutions to construct a co-jump network, and how to develop effective systemic risk metrics
based on this framework. To address these challenges, we leverage publicly available stock price data, market-level indicators,
and firm-level financial reports to assess the risk exposures faced by financial institutions. We build a Tobit-LASSO model on
individual stock jumps to identify co-jump dependence that encompasses both direct and mediated effects, and we employ this
to construct a co-jump network. Within this network framework, we define a realized systemic jump beta that measures timevarying systemic risk at both the institution and system levels. Our main empirical setting is the U.S. financial market, where we
select representative financial institutions and benchmark our approach against two established models: the conditional-CoVaR
network of Hautsch et al. (2015) and the DCC-GARCH–based MES of Brownlees and Engle (2017). We evaluate the effectiveness of
our co-jump network in tracing the evolution of system-wide risk and in assessing institutional systemic importance, and we
also explore applying the resulting systemic-risk measure to portfolio optimization. Our primary contribution is a connectivity
measure based on co-jump dependence that captures spillovers mediated through the rest of the system and simultaneously
characterizes nonlinear linkages in both upside and downside states. We further formalize a systemic risk measure within this
network and develop a portfolio strategy that integrates this measure, thereby extending the existing literature.
The remainder of this paper is organized as follows. Section 2 introduces the co-jump network framework, the proposed
systemic risk measures based on this network, and the construction of benchmark models. Section 3 describes the data and
variables used in the empirical analysis, and evaluates model performance through both qualitative and quantitative
comparisons, highlighting the unique advantages of the co-jump network approach. Section 4 discusses potential explanations
for the differences in model outcomes. Section 5 concludes.
2. Methodology
2.1. Jump detection
We consider the stock prices of
financial institutions, denoted by
, each following a jump-diffusion process of the
form:
(1)
where
and
component, where
represent the drift and diffusion terms, respectively. The last term
is a Poisson counting process and
captures the jump
denotes the jump size process. To identify jumps in individual
assets, we adopt the L-M test, which is a high-frequency intraday jump detection method based on local volatility estimation.
The core idea is to estimate the instantaneous volatility at time
using the realized bipower variation over the preceding
observations, and then construct a standardized return to assess the significance of a jump at
. The L-M test statistic is defined
as:
(2)
where the estimator for instantaneous volatility is given by:
(3)
Due to significant overnight effects in stock prices, we restrict the volatility estimation window to lie within a single trading day
to avoid mistakenly identifying overnight gaps as jumps. Following the empirical rule
, we set
accordingly. For example, under 5-minute sampling, there are
day (Lee and Mykland, 2008). Under the null hypothesis of no jumps,
distribution scaled by
with
and
observations per calendar
approximately follows a standard normal
. However, rather than using a fixed critical value, the L-M test adopts a threshold derived from
extreme value theory. Specifically, we define the standardized location and scale adjustments as:
(4)
For a significance level , the corresponding critical threshold is
, and a jump is detected at time
if:
(5)
where
denotes the number of intraday return observations per day. Compared to the jump test proposed by Barndorff-Nielsen
and Shephard (2006), the L-M test does not rely on the stability of variance estimates within a fixed window, making it more
robust for high-frequency data with strong jump localization. In the empirical analysis, we alsp employ the ABD test (Andersen et
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al., 2007) as an alternative jump-detection method to assess the robustness of our results. It is similar to the L-M test in that both
operate within a semimartingale framework, use nonparametric estimates of local volatility to standardize returns, and conduct
pointwise intraday jump identification. They differ in the decision rule: L-M constructs a significance statistic from standardized
returns, whereas ABD applies a local-volatility-based threshold-exceedance rule.
2.2. Construction of the co-jump network
Co-jump-based relations among financial institutions reflect their tail-risk synchrony and complex interdependencies.
Embedding these dependencies within a network framework allows for the simultaneous capture of both direct and indirect
linkages among financial institutions. To this end, we identify statistically significant co-jump dependencies as the basis for
network connectedness and construct a co-jump network accordingly. Existing co-jump networks are typically constructed by
computing pairwise co-jump frequencies over a given time window. However, such approaches focus solely on the simultaneity
and relative intensity of jumps while neglecting jump magnitudes and the underlying causal mechanisms. Consequently, they
are unable to assess the statistical significance of co-jump connections, differentiate the direction of risk transmission, or
account for indirect and system-wide effects. Moreover, they cannot distinguish macro-driven co-jumps from those arising from
institution-specific propagation channels. To address these limitations, we detect co-jump dependencies using the framework of
Tobit-LASSO regression.
We begin by applying the L-M jump test to each financial institution to obtain a univariate jump series that records both the
magnitude and timing of detected jumps. When multiple jumps are identified on the same day, we retain the one with the
largest absolute size. The resulting jump series for institution is defined as:
(6)
By using absolute jump magnitudes, we isolate the jump term that records whether a jump occurs and how large it is, enabling
detection of mutually exciting co-jump dependence without any ex ante sign restriction. The microfoundation for mutually
exciting jumps traces back to the Hawkes jump diffusion framework of Aït-Sahalia et al. (2015), which emphasizes the
contagious nature of jumps regardless of sign. However, this model is difficult to scale to high dimensional parametric
estimation, so it is impractical to estimate directly from price data a co-jump dependence matrix for network construction.
Therefore, we employ a Tobit-LASSO approach to identify statistically significant co-jump dependencies across assets and to
construct the co-jump network. Specifically, to examine whether the jump behavior of institution is significantly related to
other institutions (excluding common external effects), we define a covariate vector
macroeconomic state variables
institutions
for
that includes three types of variables:
, firm-specific characteristics of institution denoted
. Since
, and the jump series of all other
contains many zeros (i.e., is left-censored), we model the relationship between
and
using a Tobit regression model:
ɛ
where
(7)
ɛ
is the th element of the covariate vector
. The relevant subset of covariates in
is unknown and high-
dimensional. Identifying significant drivers of jumps requires variable selection methods that go beyond univariate significance
tests, which fail in the presence of multicollinearity, and are infeasible under joint testing with more than 60 covariates. To
overcome this, we introduce a LASSO penalty into the Tobit model to shrink coefficients of irrelevant predictors. This leads to a
sparse representation
, where only a subset of covariates is retained. While both high-dimensional regression
and censored (Tobit-type) regression have been extensively studied separately, their joint application remains limited. We follow
the Tobit-LASSO algorithm recently proposed by Jacobson and Zou (2024), which reformulates the penalized Tobit likelihood
function (Olsen, 1978) and solves it using convex optimization techniques. Specifically, the model parameters are estimated by
minimizing the following objective function:
(8)
where
is the reparameterized Tobit likelihood,
,
,
is the number of observations, and
regularization parameter. We implement this estimation using the tobitnet package in R, with the optimal
cross-validation. If
is selected by the Tobit-LASSO as a significant driver of
is the
selected via 10-fold
, this indicates that the jump of institution
makes a statistically significant conditional contribution to the jump of institution . If both
and
are selected for one
another, the linkage is bidirectional, although not necessarily symmetric. For the special case in which “opposite-direction cojumps” occur at the same instant, such hedge-like patterns would register as statistically significant and robust directed
dependence only if they were persistent and stable over time. In practice, consistent with efficient-market mechanisms, these
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relations rarely persist, especially over multi-year samples. Therefore, the Tobit-LASSO specification achieves our objective of
characterizing, within a single framework, the nonlinear tail dependence that operates in both upside and downside states.
By incorporating firm-level and macroeconomic covariates, our model can more effectively distinguish genuine contagion
channels (e.g., credit exposures, funding dependencies, business model similarities) from common external shocks. To validate
the selected predictors, we re-estimate the Tobit model for each institution using only the selected variables and compute the
fitted jump series
. Finally, significant co-jump relations identified through this procedure are used to define the network
structure. Specifically, if
is selected as a significant driver of
be the th component of
, then a directed edge from node to node is established. Let
. Formally, we define the co-jump network as:
(9)
where each node
represents a financial institution, and each directed edge
influence from to . The adjacency matrix
indicates a significant co-jump
is then given by:
(10)
2.3. Systemic risk measurement
While the topological structure of the co-jump network could offer qualitative insights into risk transmission channels and
institutional roles within the financial system, it does not provide a quantitative assessment of systemic importance at the firm
level or of the overall systemic risk level. To meet the prudential needs of systemic risk management, we extend the systemic risk
beta framework proposed by Hautsch et al. (2015) in the context of CoVaR networks, and develop a realized systemic risk beta
based on the co-jump network. Under the identified co-jump network, we evaluate each institution’s marginal contribution to
systemic risk by quantifying the marginal impact of its jumps on system-wide jumps. Specifically, we define system returns as
the market value-weighted average of institutional returns, and apply the L-M jump test to construct the system-level jump
series
. The marginal effect of institution ’s jump on the system jump at time is defined as systemic jump , formally:
(11)
where
denotes the set of drivers for
identified via the Tobit-LASSO model. To capture the time-varying nature of
assume a deterministic linear relationship with institution ’s lagged firm-specific characteristics
, we
:
(12)
where
is the coefficient vector associated with the firm characteristics. Using the previously estimated jump series
, we estimate
and
by fitting the following Tobit regression model to
ɛ
where
and
:
ɛ
(13)
includes a constant term, lagged macroeconomic state variables, and the estimated jump series
of other institutions. We define the realized systemic risk contribution of institution at time as:
(14)
This time-varying quantity can be used to rank institutions by systemic importance, thus identifying firms that are both “too big
to fail” and “too interconnected to fail”. We further define the aggregate system-wide risk measure as:
(15)
By tracking the dynamics of
, we can monitor the evolution of systemic risk and identify major systemic events in the financial
system. To validate the reliability and relevance of this systemic importance metric and its assumed time-varying structure, we
conduct a series of formal hypothesis tests. The key assumption underlying Eqs. (12) is that, conditional on macroeconomic
states and co-jump inflows, the jump of institution exerts an influence on the system-wide jump. We first test the joint
significance of all explanatory components in
under the null hypothesis:
(16)
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Next, to examine whether the marginal effect varies with firm characteristics over time, we test:
(17)
If
is not rejected, we reset
as a constant
and re-estimate the model without interaction terms, testing:
(18)
We perform Likelihood Ratio (LR) tests for
–
validity of the realized systemic risk beta. If
the time variation in marginal effects. If
. Rejection of
indicates that the model is jointly significant, supporting the
is also rejected, this implies that firm-specific characteristics significantly explain
is not rejected but
is, this indicates that the marginal effect is constant but
nonzero. To comprehensively evaluate the performance of our co-jump network-based systemic risk measure, we conduct a
comparative analysis with two benchmark models. The first benchmark (Base 1) is the CoVaR network model, which focuses on
conditional Value-at-Risk (CoVaR) connectedness among financial institutions. The CoVaR linkages are identified using a quantile
LASSO regression model. The second benchmark (Base 2) is based on the Marginal Expected Shortfall (MES), which we estimate
using a DCC-GARCH model combined with nonparametric methods. We define the market return
and institution ’s return
as:
(19)
ɛ
ɛ
ɛ
where
and
are the conditional standard deviations of market and firm returns,
correlation, and ɛ
is their dynamic conditional
are zero-mean, unit-variance, uncorrelated shocks. The joint distribution
is assumed to be bivariate
normal. The one-step-ahead MES for institution , conditional on extreme market returns below threshold
, is defined as
. Substituting from Eq. (19), we derive:
(20)
ɛ
ɛ
ɛ
The expectations in (20) are estimated nonparametrically using kernel smoothing:
ɛ
ɛ
ɛ
where
ɛ
(21)
ɛ
(22)
ɛ
is the integrated kernel function,
is the kernel function (e.g., Gaussian), and
ɛ
is the bandwidth, typically chosen as
is the estimated tail probability,
.
3. Empirical analysis
3.1. Data
This study focuses on a set of representative publicly listed financial institutions in the United States. We identify jumps in their
5-minute closing stock prices and develop econometric models to determine co-jump connectedness among institutions, based
on which we construct the co-jump network. The forward-looking nature and real-time availability of stock market data provide
a practical basis for timely and transparent monitoring of systemic financial risk. The observation window spans from January
2013 to December 2024. We classify U.S. financial institutions by Standard Industrial Classification (SIC) codes, and within each
category (Depositories, Insurance Companies, Broker-Dealers, and Others), we select the top 25 institutions by market
capitalization as the primary subjects of analysis. To account for the potential impact of macroeconomic conditions on co-jump
relationships, as well as firm-specific characteristics that may contribute to financial distress, we adopt the variable selection
framework of Hautsch et al. (2015). Specifically, we include seven macroeconomic variables and five firm-specific indicators.
Moreover, motivated by prior findings that FOMC Federal Funds Target Rate announcements (FFTRA) affect jump and co-jump
activity (Lahaye et al., 2011, Caporin et al., 2017, Gilder et al., 2014), we include an FFTRA event dummy to capture this macro
shock. Table 1 summarizes the definitions of these variables. The VIX index is obtained from the Chicago Board Options
Exchange, while the remaining macroeconomic variables, firm characteristics, and high-frequency stock data are retrieved from
the Bloomberg Terminal.
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As the jump series for financial institutions is observed at the daily level, all variables are aligned to daily frequency. Since we
also require a system-level jump measure based on intraday high-frequency data, but most publicly available financial sector
indices are reported at daily or weekly frequencies, we construct a value-weighted average price index of the selected financial
institutions to serve as a proxy for the index of the financial system. Given that balance sheet data are updated at quarterly
frequency and most accounting variables do not change smoothly over time, we do not apply cubic spline interpolation (as in
Hautsch et al. 2015) to convert quarterly data into daily frequency. Instead, we directly fill quarterly data forward into daily
values to avoid introducing interpolation-induced anomalies. To mitigate potential endogeneity, we treat the lagged
macroeconomic variables (
) and firm characteristics lagged by one quarter (
) as covariates in the model. Accordingly,
the final dataset covers the period from April 2013 to December 2024, comprising 2960 daily observations per variable. After
conducting a time-series analysis of the macroeconomic state variables, we find that all variables except for the term spread are
stationary. However, Johansen cointegration tests indicate the presence of cointegrating relationships among the macroeconomic
variables (including the term spread). Therefore, even though the term spread contains a unit root in isolation, retaining its level
form rather than differencing is justified under the cointegration framework, ensuring valid statistical inference. This treatment
is consistent with the theory of cointegrating regression consistency proposed by Pagan and Wickens (1989).
Furthermore, we restrict our sample to institutions that remain continuously present throughout the observation window,
excluding those that underwent mergers, acquisitions, delistings, or had incomplete firm-level data. After these filters, the final
sample includes 54 financial institutions, with detailed information listed in Appendix Table A1. To facilitate direct comparisons
with our benchmark models, the macroeconomic variables and firm characteristics used in Base 1 are consistent with those
presented in Table 1. Given that daily-frequency data provide more granular observations, we set the quantile level and the
exceedance loss threshold for Base 1 to 0.005, and likewise set the same threshold of 0.005 in Base 2 to determine whether the
market is in a distressed state.
Table 1. Macroeconomic variables and firm-specific characteristics.
Name
Label
Definition
Implied Volatility Index
vix
Implied volatility derived from option prices, as published by the CBOE (VIX)
Short-term Liquidity Spread
repo
Spread between 3-month USD LIBOR and 3-month U.S. Treasury bill yield
3-Month Treasury Rate Change
yield3
First difference of the 3-month U.S. Treasury bill yield
Yield Curve Slope Change
term
First difference of the spread between 10 year and 3-month U.S. Treasury yields
Credit Spread Change
credit
Yield spread between 10 year AAA-rated corporate bonds and 10 year U.S. Treasury bonds
Market Return
marketret
Daily return on the S&P 500 Index
Real Estate Return
housing
Return on the Vanguard Real Estate ETF (VNQ)
FFTRA Event Dummy
fftra
Federal funds target rate announcements
Leverage
lev
Ratio of total liabilities to total assets
Maturity mismatch
mmm
Ratio of current liabilities to current assets
Book-to-market ratio
bm
Book equity divided by market value of equity
Firm size
mc
Logarithm of market capitalization
Volatility
vol
Estimated using a GARCH(1,1) model based on daily returns
Macroeconomic variables
Firm-Specific Variables
3.2. Results of post-LASSO regressions
When the sampling frequency of asset prices is set to 5 min, there are 78 return observations per trading day. Accordingly,
following the methodology described earlier, we set the bandwidth parameter K = 20 and performed the L-M jump test. We then
estimated the Tobit-LASSO model based on the identified jump series and the Quantile-LASSO model based on exceedance loss
sequences (for Base 1), in order to identify the drivers of each financial institution’s jump behavior and Value-at-Risk (VaR),
respectively. The estimation results show that both jumps and VaR measures of financial institutions are primarily driven by
jump and exceedance loss variables of other institutions. In the presence of high-dimensional jump and loss sequences,
macroeconomic variables and firm-specific characteristics are generally not statistically significant, and therefore are not
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selected by the LASSO procedure in either the jump or VaR regressions. Table 2 presents the post-LASSO Tobit regression results
for representative institutions from each of the four industry sectors: Depositories, Insurance Companies, Broker-Dealers, and
Others, as an illustrative example of this finding. The corresponding post-LASSO quantile regression results for Base 1 are
reported in Appendix Table A2.
Furthermore, the tail risk interconnections among institutions driven by co-jumps are summarized in Table 3. For each
institution , Columns 3 and 4 of Table 3 list its direct risk drivers and direct risk recipients, respectively. The direct risk drivers
are the jump series of other institutions that are selected as relevant regressors in institution ’s Tobit-LASSO model. These
institutions are referred to as Influencing Institutions. Conversely, the direct risk recipients are institutions for which ’s jump
series is selected as a relevant regressor in their own models, and are labeled as Influenced Institutions. Additionally, we reestimate the regression models based on post-LASSO variables and report their significance levels in Table 3. As a comparison,
Table A3 in the Appendix presents the tail risk interconnections derived from CoVaR. By comparing Table 3 and Table A3, we
observe that co-jump-based tail risk linkages are notably sparser than those based on CoVaR. This is reflected in the substantially
smaller number of Influencing and Influenced Institutions per entity in the co-jump network. Since both the estimated jump
series
and the VaR series
are obtained from the re-estimated models, we also assess the overall model fit. The results
from individual significance tests suggest that the Tobit regression applied to jump sequences in our model performs better than
the quantile regression applied to returns in the Base 1 model. This implies that the regressors selected by the Tobit-LASSO
procedure possess stronger explanatory power. In contrast, the post-LASSO regressors in the quantile model frequently fail to
achieve individual significance, as only a small subset of the identified Influencing or Influenced Institutions exhibit statistically
significant coefficients in -tests.
Table 2. Exemplary post-LASSO Tobit regressions for
.
Institution
Regressor
Estimate
Std. Error
z value
Pr(
JPM
(Intercept)
−0.0133
0.0008
−16.6175
0.0000
1.1467
0.0979
11.7147
0.0000
−0.0284
0.0019
−15.1445
0.0000
2.4532
0.2553
9.6079
0.0000
−0.0169
0.0011
−15.6231
0.0000
1.4725
0.1310
11.2416
0.0000
−0.0158
0.0009
−17.0384
0.0000
0.6816
0.1394
4.8894
0.0000
0.4378
0.1007
4.3488
0.0000
0.6212
0.1600
3.8838
0.0001
0.5249
0.1411
3.7186
0.0002
LNC
MS
AXP
(Intercept)
(Intercept)
(Intercept)
Note: Regressors were selected by LASSO.
)
denotes the jump series of institution .
However, as emphasized by Hautsch et al. (2015), model fit alone is not sufficient to validate the effectiveness of the CoVaR
model. A more important criterion is whether the estimated
can accurately predict the magnitude and frequency of actual
losses, while satisfying the independent and identically distributed (i.i.d.) assumption for exceedances. To assess this, we apply
the Dynamic Quantile (DQ) test proposed by Engle and Manganelli (2004) to the VaR estimates for all institutions. The null
hypothesis of the DQ test states that the predicted VaR correctly captures the coverage rate of actual exceedances and that the
exceedances are i.i.d. The DQ test results suggest that only 24 institutions meet the required adequacy conditions (see Table A4).
This result appears to diverge from the findings of Hautsch et al. (2015), which may be attributed to differences in data frequency.
While the latter constructed its quantile regression model using weekly returns and exceedances, our model is estimated based
on daily data. At the daily frequency, volatility clustering becomes more pronounced, and the i.i.d. assumption for exceedances is
more likely to be violated due to increased noise and more frequent observations. In contrast, weekly data tend to smooth out
such noise and partially mask volatility clustering, potentially leading to better in-sample performance despite the smaller
sample size. By comparison, co-jump-based tail dependence analysis, grounded in a higher-frequency perspective, explicitly
incorporates intraday volatility risk and more accurately captures the daily dynamics of interdependence among financial
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institutions. These findings suggest that when investigating the temporal structure of financial interconnectedness at higher
resolutions, the co-jump analysis framework may provide greater robustness and reliability than the CoVaR-based approach.
Table 3. Tail risk cross dependencies driven by cojump.
Category
Institution Influencing institution(s)
Influenced institution(s)
Depositories
WFC
JPM⁎⁎⁎
OPY, AGM
JPM
MS⁎⁎⁎
WFC⁎⁎⁎, BAC⁎⁎⁎, BK⁎⁎⁎, RF⁎⁎⁎,
KEY⁎⁎⁎, MS⁎⁎⁎, AXP⁎⁎⁎, AGM
BAC
JPM⁎⁎⁎
FHI⁎⁎⁎, AGM
C
MS⁎⁎⁎
AGM
USB
TFC⁎⁎⁎
TFC⁎⁎⁎, CNA⁎⁎⁎, AXP⁎⁎⁎, AGM
COF
GS⁎⁎⁎
OPY, AGM.
PNC
GL⁎⁎⁎
GL⁎⁎⁎, AGM
BK
JPM⁎⁎⁎
MMC⁎⁎⁎, AGM
STT
NTRS⁎⁎⁎, BOKF⁎⁎⁎, MET⁎⁎⁎, CB⁎⁎⁎, L⁎⁎⁎, UNM⁎⁎ BRO⁎ RJF**
NTRS⁎⁎⁎, AGM
TFC
USB⁎⁎⁎
USB⁎⁎⁎, CMA⁎⁎⁎, MKL⁎⁎⁎,
OPY, NNI
FITB
CMA⁎⁎⁎
NNI, AGM
MTB
RF⁎⁎⁎
OPY, AGM
NTRS
STT⁎⁎⁎
STT⁎⁎⁎, OPY⁎ AGM
RF
JPM⁎⁎⁎
MTB⁎⁎⁎, ZION⁎⁎⁎, MKL, NNI,
AGM
KEY
JPM⁎⁎⁎
AGM
CMA
TFC⁎⁎⁎
FITB⁎⁎⁎, MKL, OPY., AGM
HBAN
PRU⁎⁎⁎
AGM
BOKF
UNM⁎⁎⁎
STT⁎⁎⁎, EEFT⁎⁎⁎, OPY⁎ NNI.,
AGM
Insurance
ZION
RF⁎⁎⁎
EEFT⁎ AGM
MET
PRU⁎⁎⁎
STT⁎⁎⁎, PRU⁎⁎⁎, EEFT⁎
OPY⁎⁎⁎, NNI, AGM
TRV
CB⁎⁎⁎
AFL⁎⁎⁎, CB⁎⁎⁎, BRO⁎⁎⁎, RJF⁎⁎⁎,
EEFT, OPY⁎⁎ AGM
AFL
TRV⁎⁎⁎
AJG⁎⁎⁎, OPY., AGM
PRU
MET⁎⁎⁎
HBAN⁎⁎⁎, MET⁎⁎⁎, PFG⁎⁎⁎,
LNC⁎⁎⁎, CME⁎⁎⁎, MKTX⁎⁎⁎,
AXP⁎⁎⁎, AGM
CB
TRV⁎⁎⁎
STT⁎⁎⁎, TRV⁎⁎⁎, AGM.
MMC
BK⁎⁎⁎
AON⁎⁎⁎, AGM
AON
MMC⁎⁎⁎
NNI⁎ AGM
L
HIG⁎⁎⁎
STT⁎⁎⁎, PGR⁎⁎⁎, HIG⁎⁎⁎,
CINF⁎⁎⁎, MKL⁎⁎⁎, OPY⁎ AGM.
PGR
L⁎⁎⁎
NNI⁎⁎ AGM
HIG
L⁎⁎⁎
L⁎⁎⁎, MKL⁎ AGM
PFG
PRU⁎⁎⁎
AGM
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Institution Influencing institution(s)
Influenced institution(s)
CNA
USB⁎⁎⁎
AGM
LNC
PRU⁎⁎⁎
UNM⁎⁎⁎, EEFT, OPY., AGM
CINF
L⁎⁎⁎
FNF⁎⁎⁎, MKL⁎⁎ EEFT, NNI,
AGM
BrokerDealers
UNM
LNC⁎⁎⁎
STT⁎⁎ BOKF⁎⁎⁎, EEFT., AGM
FNF
CINF⁎⁎⁎
AGM⁎⁎⁎
GL
PNC⁎⁎⁎
PNC⁎⁎⁎, AGM**
MKL
TFC⁎⁎⁎, RF, CMA, L⁎⁎⁎, HIG⁎ CINF⁎⁎ RJF⁎⁎⁎, OPY⁎ JLL⁎⁎⁎, AMG⁎⁎⁎
OPY., AGM
AJG
AFL⁎⁎⁎
AGM
BRO
TRV⁎⁎⁎
STT⁎ AGM
GS
MS⁎⁎⁎
COF⁎⁎⁎, AXP⁎⁎⁎, AGM
MS
JPM⁎⁎⁎
JPM⁎⁎⁎, C⁎⁎⁎, GS⁎⁎⁎, OPY,
AGM
CME
PRU⁎⁎⁎
AMTD
Others
NDAQ⁎⁎⁎, NNI⁎ AGM
AGM
RJF
TRV⁎⁎⁎
STT⁎⁎ MKL⁎⁎⁎, EEFT, AGM*
NDAQ
CME⁎⁎⁎
AGM
MKTX
PRU⁎⁎⁎
EEFT⁎⁎ AGM*
EEFT
BOKF⁎⁎⁎, ZION⁎ MET⁎ TRV, LNC, CINF, UNM., RJF, MKTX⁎⁎ JLL
AGM*
OPY
WFC, COF, TFC, MTB, NTRS⁎ CMA., BOKF⁎ MET⁎⁎⁎, TRV⁎⁎ AFL., L⁎ LNC., MKL., MS, AMG*
MKL⁎ AGM**
AXP
JPM⁎⁎⁎, USB⁎⁎⁎, PRU⁎⁎⁎, GS⁎⁎⁎
AGM
JLL
MKL⁎⁎⁎, EEFT, AGM
AMG
MKL⁎⁎⁎, OPY⁎ PRAA⁎⁎⁎, AGM
FHI
BAC⁎⁎⁎
NNI⁎ AGM
PRAA
AMG⁎⁎⁎
AGM
NNI
TFC, FITB, RF, BOKF., MET, AON⁎ PGR⁎⁎ CINF, CME⁎ FHI*
AGM
AGM
WFC, JPM, BAC, C, USB, COF., PNC, BK, STT, FITB, MTB, NTRS, RF, KEY, CMA, HBAN, BOKF,
OPY⁎
ZION, MET, TRV, AFL, PRU, CB., MMC, AON, L., PGR, HIG, PFG, CNA, LNC, CINF, UNM,
FNF⁎⁎⁎, GL⁎⁎ MKL, AJG, BRO, GS, MS, CME, AMTD, RJF⁎ NDAQ, MKTX⁎ EEFT⁎ OPY⁎⁎ AXP, JLL,
AMG, FHI, PRAA, NNI
*
Significance at the 5% level.
**
Significance at the 1% level.
***
Significance at the 0.1% level.
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Fig. 1. Co-jump network. Panels (a) to (e) highlight, respectively, institutions with high total degree, risk drivers, risk takers, risk
distributors, and institutions with high PageRank centrality using larger node sizes. Larger node size indicates a higher value of
the corresponding metric. Panel (f) displays the sparse co-jump network constructed using the traditional approach, with nodes
of high eigenvector centrality highlighted. Nodes are colored by institution type. (For interpretation of the references to color in
this figure legend, the reader is referred to the web version of this article.)
3.3. Qualitative analysis of the co-jump network
Fig. 1 visualizes the interconnections among financial institutions in the form of a directed network graph, illustrating which
institutions exhibit significant co-jump connectedness and the direction of these linkages. The tail dependencies implied by such
co-jump connectedness are not driven by common risk factors, thereby excluding the influence of macroeconomic conditions
such as heightened volatility, yield curve flattening, or broad-based credit deterioration. Instead, the identified risk linkages are
more likely attributable to other factors, including credit or liquidity exposures, business model similarities, or sector-specific
risk transmission channels. We begin by analyzing the network’s topological properties through degree centrality. A node’s total
degree reflects its overall level of connectedness, while in-degree and out-degree capture its functional role in risk transmission.
Based on their relative positions in the network, institutions are classified into three categories: (1) Risk Drivers are primary
sources of risk. Although they are less susceptible to contagion from others, once impacted, they tend to transmit risk to many
counterparties. A risk driver is defined as a node with out-degree at least 5 greater than its in-degree, indicating substantially
more outbound than inbound connections. (2) Risk Takers are primarily on the receiving end of risk propagation. While unlikely
to initiate systemic events, they are highly vulnerable to external shocks. A risk taker is defined as a node with in-degree at least
5 greater than its out-degree, suggesting a dominance of inbound over outbound links. (3) Risk Distributors function mainly as
intermediaries, passing on risk they receive from others. They are defined as nodes with an in-degree and out-degree difference
of no more than 1, implying a near balance between incoming and outgoing connections.
Subgraphs (a) through (d) in Fig. 1 illustrate different structural features of the co-jump network: panel (a) emphasizes
institutions with the highest total degree, while panels (b), (c), and (d) highlight risk drivers, risk takers, and risk distributors,
respectively. As shown in Fig. 1(a), Federal Agricultural Mortgage Corporation (AGM), Oppenheimer Holdings Inc. (OPY), and
Markel Corporation (MKL) are the three most connected institutions. According to Fig. 1(c), they also function as risk takers,
suggesting heightened vulnerability to risk originating from other institutions. During the sample period, AGM faced multiple
challenges, including agricultural market uncertainty, interest rate volatility, pandemic-induced economic shocks, and evolving
regulatory conditions. These factors may have adversely affected its loan quality, risk management, and overall financial health.
However, as a government-sponsored enterprise, AGM, despite being the most prominent risk taker, typically benefits from
public support during periods of financial distress, which helps mitigate potential crises. OPY, as a broker-dealer, operates across
a broad range of businesses, particularly in securities trading, investment banking, and payment processing. This diverse scope of
operations connects it to a wide array of market participants, including banks, investors, and other brokers. MKL, in contrast,
focuses on reinsurance and investment management rather than traditional insurance. Its reliance on investment income renders
it more susceptible to indirect risk transmission, especially when other insurers or its portfolio companies come under stress in
extreme market conditions.
According to Fig. 1(b), the main risk drivers include J.P. Morgan (JPM), Loews Corp. (L), The Travelers Companies, Inc. (TRV),
Prudential Financial, Inc. (PRU), and MetLife, Inc. (MET). The latter four are insurance companies, among which PRU and MET are
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globally significant life insurers. Their products, such as life, retirement, and health insurance, often involve substantial client
fund exposures, which can amplify market instability during times of crisis. As shown in Table 3, JPM’s jump series directly
influence those of WFC, BAC, BK, RF, KEY, MS, and AXP, most of which are depository institutions. This finding confirms that JPM,
as one of the largest global systemically important banks (G-SIBs), exerts discontinuous price impacts on other major banks and
key broker-dealers (e.g., MS). The influence of insurers L, TRV, PRU, and MET is even more extensive. Their risk spillovers not only
affect other insurers (e.g., HIG, PGR, CINF, MKL, CB, BRO, PFG, LNC) but also reach into depository institutions (e.g., STT, HBAN),
broker-dealers (e.g., OPY, RJF, EEFT), and other sectors such as government-sponsored enterprises (e.g., AGM). These findings
highlight the need for heightened regulatory scrutiny of such institutions due to their systemic relevance.
As shown in Fig. 1(d), most financial institutions function as risk distributors, serving as key conduits in the transmission of
systemic risk. Although these institutions may have relatively fewer connections, disruptions at these nodes can still trigger
significant systemic effects. It is important to note that being classified as a risk driver does not necessarily imply a greater
contribution to systemic risk, nor does being a risk taker imply a lesser or offsetting contribution. Our classification captures the
directionality of risk spillovers based on the topology of the co-jump network, but it does not provide a quantitative assessment
of each institution’s actual contribution to systemic risk. Furthermore, we compute the centrality of each node using the
PageRank algorithm (Brin and Page, 1998) and highlight the nodes with the highest scores in Fig. 1(e). Unlike simple degreebased measures that merely count the number of connections, the PageRank algorithm iteratively assigns weights based on the
importance of connected nodes. In other words, it accounts not only for how many connections an institution has, but also for
whether those connections originate from influential counterparts. This makes PageRank particularly effective in identifying key
nodes within the systemic risk transmission network, as it captures second- and higher-order contagion effects more accurately
than traditional in-degree or out-degree measures. As shown in Fig. 1(e), the three financial institutions with the highest
PageRank centrality are AGM, OPY, and MKL. The figure also indicates that depository institutions and insurance companies
exhibit stronger internal interconnectedness than institutions in other sectors.
We also present in Fig. 1(f) a co-jump network in which edge weights are the pairwise daily co-jump frequencies (Zhang et al.,
2024, Ding et al., 2024). We apply the minimum spanning tree (MST) to filter less important links and use eigenvector centrality
to highlight financially influential institutions. In this network, PRU, JLL, and GL tend to co-jump in sync with other core
institutions that exhibit widespread co-jumping. This pattern is better interpreted as high exposure to macro, liquidity, and
policy shocks rather than as evidence of contagion. Since the construction does not encode directionality or mediated spillover
paths, it is difficult to develop a systemic-risk metric within this framework.
3.4. Systemic risk measurement results
While network structure analysis based on node degree or centrality offers qualitative insights into a financial institution’s local
influence and position, it falls short of fully quantifying the institution’s systemic importance, namely, its actual contribution to
systemic risk. Moreover, such analysis cannot capture the time-varying nature of these contributions. This limitation motivates
the development of a systemic risk measurement framework grounded in the co-jump network. In this section, we first examine
the statistical significance of each institution’s marginal effect on the system-wide jump size. We then present realized systemic
risk contribution at the institution, sector, and system-wide levels.
As discussed in Section 2.3, the marginal effect of a financial institution’s jump on system-wide jumps may vary over time.
Accordingly, we perform a sequence of three joint hypothesis tests under the specified model:
the model used to estimate . If
is rejected, we proceed to
by firm-specific characteristics. If
is also rejected, we conduct
component of
remains after excluding interaction terms. If
tests the joint significance of
, which tests whether the time variation in
can be explained
, which examines whether a time-invariant baseline
is not rejected, the systemic risk contribution of the
corresponding institution is deemed statistically invalid. Table A5 reports the joint significance test results for the co-jump-based
systemic risk betas, while Appendix Table A6 provides the corresponding results for CoVaR-based betas. Under the co-jump
network, only one institution, NTRS, exhibits an insignificant . Additionally, nine institutions display time-invariant marginal
systemic risk effects. In contrast, under the CoVaR network, ten institutions show insignificant
time variation. The proportion of insignificant
estimates, and five exhibit no
estimates is comparable to the empirical findings of Hautsch et al. (2015),
underscoring the inherent limitations of the CoVaR-network-based approach. Taken together with the post-LASSO regression
results discussed in the previous section, these findings highlight the superior robustness and statistical validity of the co-jump
network framework.
Furthermore, we visualize the system-wide and sector-level systemic risk dynamics derived from the co-jump network, CoVaR
network, and MES over the observation window (Fig. 2). These measures are computed as the average realized systemic risk
betas of the constituent financial institutions. We set a threshold of 0.99 on the systemic risk measure to identify systemic risk
events (see 2 (a), (c), and (e)) and annotate the dates of FOMC federal funds target rate announcements. Visually, there are very
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few overlaps between the identified episodes and the FFTA dates. This indicates that our model largely filters out the influence of
external common shocks such as news announcements from the co-jump dependence structure. Accordingly, the estimated cojump dependencies and the detected systemic risk episodes do not exhibit a deterministic relationship with such major macro
announcements. Based on the clustering of these events, we divide the sample into three distinct periods: the pre-COVID period
(April 2013 to February 2020), the COVID period (March to July 2020), and the post-COVID period (August 2020 to December
2024). We then examine the evolution of systemic risk across these three phases at the aggregate, sectoral, and institutional
levels. At the aggregate level, Fig. 2(a) shows that systemic risk in the U.S. financial system remained relatively stable prior to the
COVID-19 outbreak, surged sharply during the early phase of the pandemic, and peaked within the sample window. Notably,
although systemic risk subsided somewhat in the post-pandemic phase, it remained persistently elevated relative to the prepandemic baseline, forming a “risk plateau”. This pattern suggests that the COVID-19-induced systemic shock has had lasting
effects, and the structural disruptions caused by the crisis have not been fully resolved despite a short-term market rebound. This
finding is consistent with the IMF’s 2021 Global Financial Stability Report, which emphasized the pandemic’s longer-term
implications for financial stability. Several underlying mechanisms help explain this persistence. First, ultra-loose monetary
policy, aggressive credit expansion, and the rapid rebound in asset prices during the pandemic contributed to a structural shift in
financial institutions’ risk-taking behavior. Second, while asset prices experienced a technical recovery, balance sheet repair
lagged behind, and actual capital buffer levels may not have returned to pre-pandemic norms—leaving systemic vulnerabilities
intact. Third, uncertainty regarding post-pandemic policy withdrawal heightened market sensitivity to tail risk, thereby
sustaining elevated perceptions of systemic risk. In addition, the increased activity of non-bank financial institutions and the
growing interconnectedness of the financial system further amplified the potential for contagion. Taken together, these dynamics
indicate that the pandemic not only triggered a sharp short-term spike in systemic risk, but also ushered in a new normal of
elevated systemic fragility in the medium to long term—driven by structural transformation, shifts in risk appetite, and delayed
policy normalization. However, as shown in Fig. 2(b), the CoVaR-network-based systemic risk measure fails to reflect this
structural shift. The average risk level measured by the CoVaR network remains largely unchanged before and after the
pandemic, suggesting that it may underestimate the persistence and evolution of systemic vulnerabilities following large-scale
shocks. Evidence of this transition in the MES is also muted.
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Fig. 2. Systemic risk contribution measured by three models. The first column displays the evolution of system-wide risk over
time, measured as the average systemic risk across all institutions. The red dashed line represents the 0.99 quantile of the
systemic risk measure, and red dots indicate values that exceed this threshold, signaling potential systemic risk events. The blue
dots mark the FFTRA dates. The background color blocks mark the Pre-COVID, COVID, and Post-COVID periods, each shown in a
different color. The second column shows the sector-level systemic risk, calculated as the average systemic risk within each type
of institution. Rows one to three correspond to results based on the co-jump network, CoVaR network, and MES, respectively.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
By comparing Figs. 2(a), (c), and (e), we observe that the extreme values of the systemic risk indicators based on the co-jump and
CoVaR networks are not concentrated in a single period. This suggests that, at the daily observation frequency, both measures
exhibit high sensitivity to fluctuations in the financial system’s relative risk level. As a result, a simple quantile-based threshold is
sufficient to identify historical high-pressure episodes. The two indicators yield broadly consistent identification results for
extreme events during the pre-COVID and COVID periods. However, their signals diverge significantly in the post-COVID period.
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In contrast, the extreme values of the MES are primarily concentrated during the COVID period, with relatively muted values
throughout the rest of the sample. Moreover, the MES series exhibits a highly jagged pattern, indicating that daily-frequency MES
is more susceptible to noise, which complicates the identification of systemic risk events using simple quantile-based thresholds.
Figs. 2(b), (d), and (f) illustrate the time-varying sector-level average contributions or losses to systemic risk under the three
models, respectively. According to Fig. 2(b), during the COVID and post-COVID periods, the “Other Financials” sector exhibits the
highest contribution to systemic risk, followed by Broker-Dealers and Insurance, while Depository Institutions contribute the
least. In contrast, Fig. 2(d) shows that the sectoral composition of risk remains relatively stable under the CoVaR network model
across all three periods. Broker-Dealers consistently rank first in terms of systemic contribution, followed by Others,
Depositories, and Insurance. Notably, the average realized systemic risk beta for the insurance sector turns negative in the latter
part of the COVID period. This outcome arises because we do not impose a non-negativity constraint on the estimated systemic
risk , and abrupt changes in firm-specific characteristics
may occasionally result in negative
values. If the corresponding
is large during these periods, it can drive the sector-level average realized systemic risk into negative territory. While
smoothing firm characteristics could stabilize the
estimates, it would also entail a loss of information. Following the empirical
strategy of Hautsch et al. (2015), we retain these negative values in our analysis. As shown in Fig. 2(f), the relative ranking of
average systemic losses across sectors, as measured by MES, remains largely consistent throughout the three periods. The sectors
rank, in descending order, as Insurance, Depositories, Others, and Broker-Dealers. Overall, these results reveal substantial
variation in sector-level systemic risk assessments across the three modeling approaches. In the next section, we further examine
the systemic importance rankings of individual institutions to identify potential sources of these discrepancies.
The circles in Fig. 3 illustrate the top 10 systemically important financial institutions identified by each of the three models across
the three periods. These institutions rank among the top ten based on their realized systemic risk contributions. Entities
recognized by multiple models appear at the intersections of the circles, indicating methodological consensus. According to Fig.
3, under the co-jump-network-based measure, the top 10 institutions with the highest realized systemic risk betas in the preCOVID period included four types of financial institutions, with broker-dealers being the most prevalent. During the COVID
period, however, several mid-sized institutions such as RJF, COF, and FHI (formerly known as FII) experienced sharp increases in
their systemic risk contributions as a result of the pandemic shock and subsequently entered the top 10 list. This shift reflects
how credit risk, liquidity constraints, and structural integration risks disproportionately affected mid-tier institutions during the
crisis. In the post-COVID period, as macroeconomic policy support intensified and markets gradually stabilized, the systemic risk
burden shifted back toward large, traditional financial groups such as OPY and EEFT. Meanwhile, Other Financials like AMG and
AGM emerged as significant contributors, whereas insurance companies gradually disappeared from the top-contributors list.
Across all three periods, institutions including MS, MKTX, NNI, CME, BOKF, and PRAA consistently appear among the most
systemically important entities. MS, MKTX, and CME function as market infrastructure providers or critical liquidity
intermediaries. As such, their systemic impact during periods of market stress or liquidity disruptions may be disproportionately
large relative to their market capitalization. PRAA and NNI, though nontraditional banking institutions operating on the
periphery of the credit chain, may carry elevated leverage and duration risk, amplifying shocks during tail events. These
characteristics position them as potential high-risk intermediaries during systemic stress. Similarly, BOKF, a regional commercial
bank, may face duration mismatches or hold balance sheet structures that are sensitive to interest rate movements, rendering it
more susceptible to risk spillovers under adverse market conditions.
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Fig. 3. Systemically important institutions identified by the three models. Panels (a)–(c) correspond to the identification results
for the three time periods. Each colored circle lists the top 10 financial institutions in terms of systemic risk contribution as
identified by each model. (For interpretation of the references to color in this figure legend, the reader is referred to the web
version of this article.)
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In the CoVaR-network-based systemic risk measures, the top 10 institutions with the highest realized systemic risk betas across
all three periods are primarily broker-dealers, such as RJF and MS. Depository institutions like WFC and BOKF also emerge as
stable and influential contributors, while insurance companies account for the smallest share among the top contributors. In
contrast, the MES-based rankings identify insurance firms, such as MET, MKL, and L, as the most systemically important
institutions. Fig. 3 reveals several key insights. First, the ranking of systemically important institutions based on the co-jump
network exhibits substantial differences across the three periods, while the rankings derived from the CoVaR network and MES
remain relatively consistent over time. This indicates that the co-jump-based approach is more sensitive to the time-varying
structure of the financial system. Second, the co-jump-based rankings show partial overlap with those generated by both
baseline models. This suggests that the co-jump method integrates the strengths of the MES approach, which emphasizes an
institution’s contribution to system-wide losses, and the CoVaR approach, which focuses on the structure of financial
interdependencies. This observation indirectly supports the validity of the co-jump model. In comparison, the rankings from the
CoVaR network and MES show little overlap. Third, the measure of systemic importance provides insights beyond what is
captured by the network structure alone. A comparative analysis of the ranking results and the PageRank scores derived from the
two networks reveals no clear correlation, as shown in Fig. 4. In the alternative specification, we identify jumps using the ABD
test and replicate the empirical procedure described above. The results show that, across the two jump-detection methods (ABD
and L-M), the sets of risk drivers, risk takers, and risk distributors are broadly consistent, indicating a robust overall network
structure. More than 80% of the systemic risk events identified by the two tests overlap. Sectoral shares of systemic risk
contributions exhibit similar time profiles, and the aggregate level of systemic risk shows a structural increase in the post COVID
period. In the pre COVID, COVID, and post COVID subperiods, the overlap of the top ten most systemically important institutions
identified by the two tests exceeds 70%. Taken together, these results support the robustness of our framework to alternative
intraday jump-detection schemes. Based on the joint significance tests, under the L-M specification only the
whereas under the ABD specification, BRO, JLL, and AMTD fail
for NTRS fails
,
, which suggests that L-M is the preferable testing approach. In
light of this comparison, we retain the LM-based main results in the text and relegate the ABD-based results to the Appendix (see
Figs. A1 to A3 and Table A7).
The foregoing analysis is conducted from a supervisory perspective, so the primary application is macroprudential oversight.
From an investor’s perspective, the proposed systemic risk measure can also support portfolio strategy optimization. We propose
a portfolio optimization strategy that embeds the systemic jump beta into a mean–variance (MV) framework. At each
rebalancing date t, we estimate the daily mean
and covariance
using a fixed rolling window
we compute the one-step-ahead, institution-level systemic jump beta
center it,
and obtain the adjusted covariance
. Based on
(via
. In parallel, using Eq. (12),
. We convert this beta to a percentile score and de-
, we construct a diagonal scaling matrix
). We then solve
, subject to the same investable universe,
bounds on weights, and transaction-cost settings as the benchmark, and implement the resulting weights at
of-sample returns. The benchmark strategy differs only in that it replaces
with the original
to obtain out-
. Unlike Bonaccolto et al. (2022)
and Zhang et al. (2024), which rebuild a network within each rolling window, our approach obtains
directly at time and
embeds systemic jump beta into the risk matrix without repeatedly reconstructing the network. Conceptually, the optimization
re-prices exposure to the systemic jump factor so that portfolio weights tilt away from high-exposure assets toward lowexposure assets. This should, in principle, help contain tail losses and drawdowns, while potentially sacrificing some upside
during strong rallies, making it a more defensive strategy.
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Fig. 4. PageRank centrality vs. network-based systemic risk. The first row and second row present results from the co-jump
network and CoVaR network, respectively. Each column corresponds to a different time period.
Empirically, we split the historical sample into a 60–40 training and testing period. Using high-frequency data in the training
window, we construct the co-jump network and estimate the relevant parameters. On this basis, in the testing window we obtain
day by day, estimate (
,
) with a rolling procedure, and solve for portfolio weights. Portfolio weights are updated at a
weekly frequency in the baseline setting. We then compare the out-of-sample performance of the enhanced MV strategy with
the benchmark MV strategy. We visualize cumulative returns and drawdowns in Fig. 5, and we evaluate both strategies using
annualized return, annualized volatility, the Sharpe ratio, maximum drawdown, and
(see Table 4). These results are
net of proportional transaction costs charged on both buys and sells at each rebalancing. Specifically, we deduct costs as
where is the proportional transaction-cost rate (baseline
is two-way one-period turnover, where
,
under the two-way convention) and
denotes the pre-trade (drifted) portfolio weights right
before rebalancing. Table 4 also reports portfolio turnover for both strategies (mean and distributional statistics of one-period
turnover).
From the reported results, our strategy increases annualized return by about 7%, reduces losses by roughly 56%, lowers
annualized volatility by about 3 percentage points (approximately an 14% decline), reduces maximum drawdown by about 37%,
and tightens
by about 14%. Although the Sharpe ratio remains negative, it improves by 0.37. These findings indicate
that the strategy materially reduces left-tail risk and drawdowns while mitigating overall losses, consistent with its intended
defensive profile. The results remain robust when we re-evaluate performance under alternative transaction-cost assumptions (
, 5, and 10 bps) and under an alternative rebalancing frequency (monthly instead of weekly); see Appendix Table A8 for
details. Taken together, these results confirm the value of measuring systemic risk via the co-jump network for macroprudential
monitoring and for portfolio strategy optimization.
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Fig. 5. Out-of-sample performance of the benchmark and enhanced mean–variance strategies.
Table 4. Out-of-sample performance and portfolio turnover: benchmark vs. enhanced mean–variance strategy.
Ann. Ret.
Ann. Vol.
Sharpe
MaxDD
Turnover (two-way)
Mean
Median
q25%
q75%
q95%
Standard MV
−12.88%
17.12%
−0.75
56.88%
−0.0245
2.36%
1.89%
1.57%
2.28%
2.94%
Enhanced MV
−5.70%
14.71%
−0.39
35.74%
−0.0211
5.80%
3.94%
2.09%
8.18%
12.18%
4. Discussion
In this section, we investigate the possible reasons for the discrepancies observed in Fig. 2, Fig. 3 by examining three dimensions:
core concepts, reflection mechanisms, and economic implications. From a conceptual standpoint, the co-jump framework
emphasizes synchronous, discontinuous jumps in the price processes of financial institutions over short time intervals. In
contrast, the CoVaR network framework captures the simultaneous occurrence of loss exceedances across institutions, while MES
focuses exclusively on the co-movement between individual institutions and the market during episodes of extreme negative
returns. Regarding reflection mechanisms, the co-jump model captures tail risk dependencies arising from abrupt price
movements, such as intraday spikes or drops that may not be reflected in daily return extremes. CoVaR, by contrast, reflects tail
dependencies based on extreme daily returns, often associated with sustained price trends. Moreover, the CoVaR model does not
jointly capture dependencies arising from both upward and downward movements. Similarly, MES captures one-sided tail
dependence between an institution and the market, focusing only on downside risk. In terms of economic interpretation, the cojump network model reveals tail co-risk exposures among institutions after filtering out common external factors. These cojumps may arise from idiosyncratic leverage channels, investor herding, or sudden shocks such as localized defaults, block trades,
credit events, or flash crashes. While the CoVaR network also emphasizes network-based tail co-risk, it tends to overlook
discontinuous shocks, which may lead to biased systemic risk estimates. In contrast, MES estimates an institution’s marginal
expected shortfall but accounts only for direct exposure, neglecting network externalities, namely, the cascading effects of interinstitutional linkages. The 2008 global financial crisis not only exposed the structural vulnerabilities of the financial system but
also underscored the central role of interconnectedness in risk propagation. Therefore, systemic risk measures that fail to
incorporate network effects may fall short of meeting current prudential regulatory requirements.
Building on the above analysis, we find that systemic risk measurement under the co-jump network framework offers distinct
advantages over the benchmark models (CoVaR-network and MES) in both model significance and practical effectiveness. In
terms of statistical significance, the co-jump-based models outperform CoVaR-network in both post-LASSO regressions and
systemic beta estimations, as demonstrated by the results of individual and joint significance tests. This statistical robustness
enhances the interpretability and credibility of the resulting risk estimates. With respect to effectiveness, co-jump-based
systemic risk measures more accurately capture structural changes in the U.S. financial system during the post-COVID period and
are highly responsive to daily fluctuations, thereby providing regulators with a more timely and reliable monitoring tool.
Additionally, cross-model comparisons show that institutions identified as systemically important by the co-jump framework
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exhibit consistency and better reflect the evolving roles of institutions within the financial system across different periods.
Overall, the practical takeaway is that the co-jump network offers an event-oriented complement to CoVaR-network and MES,
which primarily focus on one-sided tail-risk conditions. It is particularly useful for monitoring systemic risk that propagates
through abrupt price changes, whether positive or negative, and through interconnectedness. This comes with a trade-off, since
the approach relies on high-frequency intraday data and jump-identification procedures, thereby increasing model complexity
and raising the bar for data availability. For slow-moving, trend-driven distress that accumulates gradually over time, CoVaRnetwork and MES can already provide informative signals.
5. Conclusion
Analyzing the interconnectedness of financial institutions through a network framework has become a standard approach to
quantifying systemic financial risk. However, a central challenge in this perspective lies in representing financial network
connectivity in a parsimonious, timely, and empirically feasible manner, while adequately accounting for the system’s inherent
complexity and dynamics. Given that co-jumps in financial institutions’ stock prices are closely aligned with the defining
characteristics of systemic risk in terms of their nature, origins, and transmission pathways, and that co-jumps can be identified
using publicly available, real-time market data, we propose a co-jump-based connectedness indicator. We construct the
corresponding co-jump network, develop a systemic risk measurement framework based on it, and apply the approach to the
U.S. financial market. This initiative seeks to address three key tensions between prevailing theoretical models of financial risk
networks and the practical demands of systemic risk measurement: (1) The need to uncover hidden risk transmission channels
among financial institutions vs. the inaccessibility of internal data. Inter-institutional risk linkages are often embedded in capital
flows and credit exposures, which are rarely disclosed publicly and typically subject to reporting lags. Consequently, there is a
pressing need for empirically viable approaches that reveal these latent connections using observable market data. (2) The need
to capture both upward and downward tail dependencies vs. the limitations of existing network connectedness metrics.
Traditional linear dependence measures fail to capture risk co-movements under extreme conditions, and existing taildependence approaches generally focus only on downside risks. This neglects the systemic implications of upside comovements, which may signal speculative bubbles. Accordingly, there is a need for network-based indicators capable of
capturing both left- and right-tail dependencies, to better reflect the nonlinear and abrupt amplification mechanisms that arise
in stress scenarios. (3) The need to quantify systemic risk levels vs. the structural limitations of existing co-jump network
models. Although co-jumps in asset prices offer a theoretically grounded and empirically tractable lens for depicting financial
interconnectedness, existing models are largely restricted to pairwise jump synchrony analysis. This limits their ability to
quantify systemic risk or trace spillover pathways across the network, rendering them inadequate for robust, policy-relevant
systemic risk assessment.
The co-jump network framework proposed in this paper not only satisfies the need to capture both left- and right-tail
dependencies, but also enables the identification of latent interconnections among financial institutions without relying on
confidential data. Moreover, it moves beyond the traditional paradigm of pairwise relationship analysis. Empirical evidence
based on U.S. financial market data shows that the co-jump network is particularly well-suited for detecting time-varying tail
dependencies among financial institutions at the daily observation level. Compared to benchmark models, the CoVaR-based
network and the MES model, the co-jump network exhibits greater robustness and effectiveness in measuring systemic risk. It
captures structural shifts in the system-wide risk level of the U.S. financial system during the post-COVID period and identifies
liquidity providers and highly leveraged financial intermediaries as the primary contributors to systemic risk. Furthermore,
during the pandemic, several mid-sized financial institutions experienced substantial increases in their realized systemic risk
contributions due to shocks related to credit risk, liquidity constraints, and structural integration risk. Both the co-jumpnetwork-based and CoVaR-network-based measures indicate that insurance companies are underrepresented among the top ten
systemically important institutions. This stands in stark contrast to the results from the MES model, where insurers dominate the
top ranks. This discrepancy suggests that models focusing solely on stock price dynamics, while ignoring network
interconnections and balance sheet structures, may overestimate the systemic importance of insurance firms. The empirical
results further show that the mean–variance strategy augmented with our systemic risk measure helps avoid extreme downside
losses. This indicates that the optimization re-prices exposure to the systemic jump factor, automatically shifting portfolio
weights from high-exposure assets toward low-exposure assets. These findings highlight the method’s dual economic relevance
for both regulators and investors.
In future research, we plan to explore more complex modeling settings, such as incorporating nonlinear effects of explanatory
variables on the tail dependence structure captured by co-jumps. This involves moving beyond linear regression models for
identifying significant co-jump linkages and integrating richer firm-level and market-level information to improve the
effectiveness of systemic risk measurement. We also aim to extend the proposed framework to analyze systemic risk in emerging
financial markets and to identify cross-border risk transmission channels. From a technical perspective, we plan to impose
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certain constraints on the model to ensure that time-varying marginal effect indicators remain stable in the presence of abrupt
changes in firm characteristics, thereby avoiding negative values that may otherwise distort interpretation. In parallel, we aim to
relax current data limitations and enrich the covariate set with additional institution-level event variables, such as rating changes
and Form 8-K disclosures.
Funding
This work was supported by the China Postdoctoral Science Foundation (Grant Number: 2025M780768).
Declaration of competing interest
The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.
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Data will be made available on request.
Replication Package for article ‘‘A Co-Jump Network Approach to Systemic Risk Measurement: Evidence from
the U.S. Financial Market’’, includes readme file, main code and data. (Original data)
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Acknowledgments: We thank the anonymous referees for their constructive comments.
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