Empirical study of components of
Eurozone sovereign bond and CDS
spreads within joint
non-parametric modeling framework
Victor Lapshin, Marat Kurbangaleev
Laboratory for Financial Engineering and Risk-Management
Higher School of Economics
Problem
• Bond yields depend on a wide range of factors.
• In practice a number of factors is reduced to 2 or 3
components, such as a zero-coupon yield, a credit risk
and a liquidity.
• In some cases yields may be decomposed
consecutively starting with a zero-coupon yield curve.
• In other cases components may not be identified
separately, so an additional information on
components is required (for example, prices of credit
derivatives). This is the case of Eurozone sovereign
bond market.
2
Motivation
• Decomposition of bond yields in different
circumstances/environment may require
different methods and information.
• Popular models are too primitive to describe
complex but plausible curves and inflict errors.
• Components may be use for pricing and
hedging strategy building.
3
Bootstrapping hazard rates for
Greece (20th June 2011)
4
Fitting yield curve for Greek bonds with
popular methods (19th April 2011)
5
Literature Review
• Reduced-form models
– Consecutive estimation
• Longstaff et al. (2005): CDS is “pure” credit risk premium.
• Chen et al. (2008): liquidity premium is earned by CDS buyer,
CDS ask quote is free from liquidity effect.
– Simultaneous estimation
• Buhler and Trapp (2009): CDS bid and ask quotes are driven
by correlated processes.
• Econometric models
• Calice et al. (2011) follow model-independent approach in
measuring credit and liquidity component and use timevarying vector autoregression framework to establish the
credit and liquidity spread
6
Contribution
•
•
•
•
Panel data.
Advanced original methodology.
Joint estimation procedure.
Cross-market liquidity, which is measured
by CDS-bond spread, is taken into
account, while individual characteristics
of liquidity are used as accuracy
measures for estimation procedure.
7
Interest Rate and Credit Risk Analogies in
Reduced-Form Model
• An economic sense dictates the following
requirements to discount function d (t , s ) for any t :
1.
2.
3.
4.
d (t , s1)  d (t , s 2) if s1  s 2
d (t , s )  0, for  s  0
d (t , 0)  1
d (t , s )  0, with s  0
where t is moment of time and s is term.
• In reduced-from models the same properties are
required from survival probability function P( t , s ) .
8
Interest Rate and Credit Risk Analogies in
Reduced-Form Model
• The main object modeled within reduced-form
models of interest rates is a term structure of
instantaneous forward rates ft ( s ). Discount factor
s
is:
s r (s)
 f ( ) d
d (t , s)  e
t
e

t
0
• In context of a credit risk a corresponding object
is a term structure of hazard rates t ( s ) , which
are in essence a densities of probability to have a
default at term s conditional on information
available at time t. Hence survival
probability is:
s
P(t , s)  e 0
 t ( ) d
9
Double HJM Equations
• The joint uncorrelated model


~ j d j


dr

Dr


dt



t
t
t
t
 t
j 1



~j
j
~ dt 
~
d  D  
 t d t

t
t
t

j 1

gives a nonparametric approach to snapshot yield
curve and default intensity fitting.
• Infinite-dimensional model is needed because it
serves as a guarantee for the approach to be
internally consistent and arbitrage-free for use on
an everyday basis
10
Joint estimation of hazard rates
and interest rate
• Find a risk-free spot forward rate curve f(t)
and issuer-specific spot hazard rates hi(t) such
that:
– CDS quotes are fitted with weights proportional to
relative liquidity.
– Risky bonds prices are fitted with weights
proportional to bid-ask spreads.
– Fitted curves are sufficiently smooth.
11
Joint estimation of hazard rates
and interest rate
Optimization problem:


  f '( )2 d   J1k     hk ( )2 d    J 2k  min
k
where
1
J  k
k
T askT  bidT
k
1
k
k
f (·), hk (·)
 K 

T
k
 PT    d (ti ) Fi ,T Qk (Ti )  0 (1-LGD)·d ( )d 1  Qk ( )  

 i 1

Nk ,T
2
N
T
 T

k
k
J 2   wT   LGD·d ( )d 1  Qk ( )   sT  d (Ti ) (Ti 1, Ti )Qk (Ti )   d ( ) (TI ( ) , )d 1  Qk ( ) 
0
T
i 1
0

12
2
Data
• Eurozone sovereign bonds price data:
• Market price
• Bid & Ask
• Source: Bloomberg
• Eurozone sovereign CDS price data:
• Conventional spreads / par spreads
• Source: Reuters
• Issuers: Germany, France, Italy, Spain, Ireland, Greece,
Portugal
• Time period: March 2010 – June 2011
13
Results (France)
14
Results (Portugal)
15
Results (Portugal)
16
Results (Greece)
17
Results (Greece)
18
Conclusions
• Hazard rate term structure indicates two scenarios of
evolution of reference entity’s credit quality.
• While term structures of risk-free yield and hazard
rates have quite regular shapes, the bond-CDS basis
which we treat as cross-market liquidity spread evolves
in rather non-trivial but pronounced manner.
• Liquidity of CDS market dries up from longer tenors
with decline in credit quality of reference entity.
• Significant liquidity squeeze in CDS market during
continuous time span.
19
Acknowledgements
• The study was implemented in the framework
of the Basic Research Program at the National
Research University Higher School of
Economics (HSE) in 2012.
20
mkurbangaleev@hse.ru