How far do shocks move across borders?
Examining volatility transmission in major
agricultural futures markets
Manuel A. Hernandez, Raul Ibarra, and Danilo R. Trupkin
IFPRI, Banco de Mexico, and Universidad de Montevideo
Workshop on Food Price Volatility and Food Security
Bonn, January 31, 2013
Introduction
Model
Data
Results
Conclusions
Motivation
Objective
Motivation
In recent years, we have been witness to dramatic increases in both
the level and volatility of international agricultural prices.
This has raised concern about unexpected price spikes as a major threat to
food security, particularly in less developed countries.
Similarly, (1) the important development of futures markets and (2)
their major informational role, have contributed to the increasing
interdependence of agricultural markets.
E.g., the average daily volume of corn futures traded on a regular session in
CBOT is around 80-90k (compared to 20k 25 years ago).
Lead-lag relationships suggest that spot prices move toward futures prices
(Garbade & Silver, 1983; Crain & Lee, 1996; Hernandez & Torero, 2010).
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Motivation
Objective
Motivation (2)
Identifying the ways in which international futures markets interact
can provide important insights for further understanding global food
price volatility.
The analysis can also provide additional information to the ongoing
debate about the potential regulation of futures exchanges.
a
Shock
Exchange B
Exchange A
Shock
b
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Motivation
Objective
Objectives
We evaluate the level of interdependence and volatility transmission
between leading agricultural futures exchanges (volume).
United States (Chicago)
Europe (France, UK)
Asia (China, Japan)
Focus on three key commodities:
Corn
Wheat
Soybeans
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Motivation
Objective
Objectives (2)
Estimate two Multivariate GARCH (MGARCH) models to explore
futures markets interactions in terms of the conditional second
moment (better insight about dynamic price relationship).
BEKK, Engle and Kroner (1995)
Dynamic Conditional Correlation (DCC), Engle (2002)
We want to address the following specific questions:
Is there volatility transmission across markets?
What is the magnitude and source of interdependence between markets?
How does a shock (innovation) in a market affects volatility in other
markets?
Has the level of interdependence changed across time?
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Conditional Mean
Conditional Variance
Conditional Mean Equation
yt
=
Θ0 +
p
X
Θj yt−j + εt ,
j=1
εt |It−1
∼ (0, Ht )
{yt } 3 × 1 vector of daily returns at time t for each market n, i.e.,
yt = log(Pt /Pt−1 ).
Θ0 3 × 1 vector of long-term drift coefficients.
Θj 3 × 3 matrix of parameters.
εt 3 × 1 vector of errors conditional on past information It−1 .
Ht 3 × 3 matrix of conditional variances and covariances.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Conditional Mean
Conditional Variance
BEKK Model
Suitable to characterize volatility transmission across markets since
flexible enough to account for own- and cross-volatility spillovers and
persistence.
Ht = C 0 C + A0 εt−1 ε0t−1 A + B 0 Ht−1 B
cij Elements of upper triangular matrix of constants C .
aij Measure the degree of innovation from market i to market j.
bij Measure the persistence in conditional volatility between markets i y
j.
By construction, Ht is positive definite.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Conditional Mean
Conditional Variance
BEKK Model (2)
Conditional Variance Equation for Market 1:
2
2 2
2 2
2 2
h11,t = c11
+ a11
ε1,t−1 + a21
ε2,t−1 + a31
ε3,t−1
+ 2a11 a21 ε1,t−1 ε2,t−1 + 2a11 a31 ε1,t−1 ε3,t−1 + 2a21 a31 ε2,t−1 ε3,t−1
2
2
2
+ b11
h11,t−1 + b21
h22,t−1 + b31
h33,t−1
+ 2b11 b21 h12,t−1 + 2b11 b31 h13,t−1 + 2b21 b31 h23,t−1 .
Markets are both directly and indirectly related through spillovers and
persistence.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Conditional Mean
Conditional Variance
DCC Model
Suitable to evaluate if the degree of interdependence between markets,
measured through a conditional correlation matrix Rt , has changed across
time.
H t = D t R t Dt
−1/2
Rt = (ρij,t ) = diag (qii,t
Qt = (1 − α − β)Q̄ +
1/2
−1/2
)Qt diag (qii,t
0
αut−1 ut−1
).
√
+ βQt−1 , uit = εit / hiit .
1/2
Dt = diag (h11t ...hNNt ).
hiit GARCH(1,1) specification, i.e. hiit = ωi + αi ε2i,t−1 + βi hii,t−1 .
Q̄ N × N unconditional variance matrix of ut .
α, β non-negative scalar parameters satisfying α + β < 1.
Essentially Qt is a VMA process that captures short-term deviations in the correlation
around its LR level. Rt sheds light on how markets are interrelated in the SR and LR.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Data
The Asynchronous Problem
Data
Daily closing prices 2004-2009 (Commodity Research Bureau,
Futures database).
Corn: Chicago (CBOT), France (MATIF), China (DCE).
Wheat: Chicago (CBOT), UK (LIFFE), China (ZCE).
Soybeans: Chicago (CBOT), China (DCE), Japan (TGE).
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Data
The Asynchronous Problem
Data (2)
We work with the nearby contract (Crain & Lee, 1996).
Are the most active, liquid contracts and contain more information.
Consider only those days where all markets were open.
All prices are standardized to US dollars per MT (account for
exchange rate).
We work with daily returns, y = log (Pt /Pt−1 ), to obtain a
convenience support for the distribution of error terms.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Data
The Asynchronous Problem
Daily returns
Corn
Wheat
Soybeans
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Data
The Asynchronous Problem
The Asynchronous Problem (corn)
Period t-1 (Day 1)
Period t (Day 2)
GMT
(World time) 24:00
DCE
(local time in 9:00
China)
24:00
ydu,t
15:00
24:00
9:00
15:00
Price Return
in DCE
MATIF
(local time in
France)
10:45
yfu,t
18:30
9:30
18:30
Price Return
in MATIF
ξf,t-1
CBOT
(local time in the
United States)
10:45
13:15
ycu,t
9:30
ξf,t
13:15
Price Return
in CBOT
We need to account for potential bias when considering exchanges with different closing times
(synchronize data by exploiting information from markets that are open to derive estimates for
prices when markets are closed).
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Data
The Asynchronous Problem
Synchronizing the returns (Engle and Rangel, 2009)
1
The asynchronous returns, yt = log(Pt ) − log(Pt−1 ), are modeled as
a VMA(1):
yt = νt + Mνt−1 , Vt−1 (νt ) = Hν,t
M Moving average matrix.
νt Unpredictable component of the return, i.e., Et (yt+1 ) = Mνt .
2
If P̂t = Et (Pt+1 ), the synchronized returns ŷt can be defined:
ŷt = Et (log(Pt+1 )) − Et−1 (log(Pt ))
= νt + Mνt .
The synchronized returns and covariance matrix are, then, estimated:
ŷt
=
(I + M̂)νt ,
Vt−1 (ŷt )
=
(I + M̂)Ĥν,t (I + M̂)0
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
T-BEKK Results
Coefficient
ci1
Corn
DCE
(i=3)
CBOT
(i=1)
LIFFE
(i=2)
ZCE
(i=3)
CBOT
(i=1)
DCE
(i=2)
TGE
(i=3)
0.377
(0.107)
-0.036
(0.163)
-0.037
(0.083)
0.040
(0.245)
-0.119
(0.048)
0.036
(0.238)
0.115
(0.421)
0.430
(0.152)
-0.018
(0.028)
0.204
(0.030)
0.065
(0.166)
0.011
(0.009)
0.983
(0.012)
-0.086
(0.111)
0.135
(0.048)
0.081
(0.183)
-0.072
(0.104)
0.995
(0.008)
-0.017
(0.041)
-0.058
(0.254)
0.043
(0.026)
0.199
(0.068)
-0.066
(0.108)
0.001
(0.003)
0.976
(0.014)
-0.066
(0.334)
-0.333
(1.029)
0.360
(0.640)
0.410
(1.149)
0.055
(0.042)
-0.125
(0.068)
0.526
(0.086)
0.004
(0.031)
0.037
(0.033)
-0.398
(0.402)
-0.001
(0.026)
0.156
(0.048)
0.091
(0.067)
0.098
(0.071)
0.971
(0.014)
-0.003
(0.013)
0.009
(0.032)
0.085
(0.542)
-0.070
(0.860)
0.367
(0.269)
0.041
(0.035)
-0.025
(0.041)
0.638
(0.092)
0.004
(0.043)
0.029
(0.023)
0.608
(0.072)
0.129
(0.042)
-0.182
(0.070)
0.026
(0.021)
0.918
(0.025)
0.186
(0.062)
0.005
(0.007)
0.198
(0.084)
0.232
(0.121)
-0.033
(0.021)
0.047
(0.025)
0.759
(0.066)
0.003
(0.009)
0.140
(0.525)
0.079
(0.104)
0.229
(0.305)
0.073
(0.079)
-0.194
(0.126)
0.206
(0.048)
-0.055
(0.044)
0.088
(0.095)
0.979
(0.013)
ci3
ai2
ai3
bi1
bi2
bi3
Soybeans
MATIF
(i=2)
ci2
ai1
Wheat
CBOT
(i=1)
Wald joint test for cross-volatility coefficients on each commodity (H0 : aij = bij = 0, ∀i 6= j)
Chi-sq
31.600
63.060
p-value
0.002
0.000
Wald test for non causality in variance on each market (H0 : aij = bij = 0, ∀j, i 6= j)
Chi-sq
3.497
3.831
8.192
6.182
9.142
14.479
8.396
p-value
0.478
0.429
0.085
0.186
0.058
0.006
0.078
Log likelihood
# observations
-5,169.3
1,105
Hernandez, Ibarra and Trupkin
40.479
0.000
12.154
0.016
6.931
0.140
-4,857.0
-6,696.7
960
1,227
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
Corn: IR analysis
The responses are the result of a 1%-innovation in the own conditional volatility of the market
where the innovation first occurs. The responses are normalized by the size of the original shock.
CBOT Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-10
0
10
20
30
h11 (CBOT)
40
50
60
h22 (MATIF)
70
80
90
h33 (DCE)
MATIF Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-10
0
10
20
30
h11 (CBOT)
40
50
60
h22 (MATIF)
70
80
90
h33 (DCE)
DCE Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-10
0
10
20
30
h11 (CBOT)
40
50
60
h22 (MATIF)
Hernandez, Ibarra and Trupkin
70
80
90
h33 (DCE)
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
Wheat: IR analysis
The responses are the result of a 1%-innovation in the own conditional volatility of the market
where the innovation first occurs. The responses are normalized by the size of the original shock.
CBOT Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-20
0
20
40
h11 (CBOT)
60
80
100
h22 (LIFFE)
120
140
160
180
h33(ZCE)
LIFFE Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-20
0
20
40
h11 (CBOT)
60
80
100
h22 (LIFFE)
120
140
160
180
h33(ZCE)
ZCE Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-20
0
20
40
h11 (CBOT)
60
80
100
h22 (LIFFE)
Hernandez, Ibarra and Trupkin
120
140
160
180
h33(ZCE)
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
Soybeans: IR analysis
The responses are the result of a 1%-innovation in the own conditional volatility of the market
where the innovation first occurs. The responses are normalized by the size of the original shock.
CBOT Shock
2.0%
1.5%
1.0%
0.5%
0.0%
-10
0
10
20
30
40
h11 (CBOT)
50
60
70
80
70
80
h22 (DCE)
DCE Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-10
0
10
20
h11 (CBOT)
30
40
50
60
h22 (DCE)
h33 (TGE)
TGE Shock
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-10
0
10
20
h11 (CBOT)
30
40
h22 (DCE)
Hernandez, Ibarra and Trupkin
50
60
70
80
h33 (TGE)
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
T-BEKK Results (Summary)
The results confirm the importance of Chicago in global agricultural markets,
despite the increase in the production of corn-based ethanol and regulations &
trade policies governing agricultural products.
It is interesting to observe that CBOT has spillover effects over China, a closed,
highly regulated market; China also has spillover effects over other exchanges (at
least for soybeans).
The fast adjustment process after own- and cross innovations in Chinese markets
further support the robustness of our estimations.
Now, is there a higher market interdependence?
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
Dynamic Conditional Correlations (T-DCC Model)
Corn
Correlation CBOT-DCE
Correlation MATIF-DCE
0.5
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
0.1
0.0
Sep-04
Mar-05
Sep-05
Mar-06
Sep-06
Mar-07
Sep-07
Mar-08
Sep-08
Mar-09
Sep-08
Mar-09
0.5
Sep-07
Mar-08
0.6
Sep-06
Mar-07
0.6
Sep-05
Mar-06
0.7
0.6
Sep-04
Mar-05
0.7
-0.1
Sep-04
Mar-05
Sep-05
Mar-06
Sep-06
Mar-07
Sep-07
Mar-08
Sep-08
Mar-09
Correlation CBOT-MATIF
0.7
Wheat
Correlation CBOT-LIFFE
Correlation CBOT-ZCE
Correlation LIFFE-ZCE
0.7
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
0.0
-0.1
-0.1
-0.1
0.2
May-05
Oct-05
Mar-06
Aug-06
Jan-07
Jun-07
Nov-07
Apr-08
Sep-08
Feb-09
May-05
Oct-05
Mar-06
Aug-06
Jan-07
Jun-07
Nov-07
Apr-08
Sep-08
Feb-09
May-05
Oct-05
Mar-06
Aug-06
Jan-07
Jun-07
Nov-07
Apr-08
Sep-08
Feb-09
0.1
Soybeans
Hernandez, Ibarra and Trupkin
Feb-08
Sep-08
Apr-09
Dec-06
Jul-07
Jul-07
Apr-09
Feb-08
Sep-08
Dec-06
May-06
Oct-05
Jan-04
Mar-05
Aug-04
Apr-09
Sep-08
Jul-07
0.2
Feb-08
0.3
0.2
Dec-06
0.3
0.2
May-06
0.4
0.3
Oct-05
0.5
0.4
Jan-04
0.6
0.5
0.4
Mar-05
0.6
0.5
Aug-04
0.6
Jan-04
Correlation DCE-TGE
0.7
Aug-04
Mar-05
Correlation CBOT-TGE
0.7
Oct-05
May-06
Correlation CBOT-DCE
0.7
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Full sample
Variation across time
Robustness
Sensitivity
1
Segmented our sample based on structural break tests for volatility
(1st half 2008): pre- and post-crisis.
Cross-effects stronger for corn and slightly weaker for wheat in post-crisis;
no major change in soybeans (resemble DCC results).
2
In wheat, we find very similar results when considering Kansas
(KCBT) instead of Chicago (CBOT).
3
Evaluated robustness of results when excluding China (regulated
market with lower time-varying conditional volatility).
Both the BEKK and DCC results are qualitatively similar to the base
results.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Introduction
Model
Data
Results
Conclusions
Summary
Wrapping up
The agricultural markets analyzed are highly interrelated.
Higher interaction between Chicago and both Europe and Asia than
between the latter.
Chicago plays a major role in terms of spillover effects, particularly
for corn and wheat (no decoupling of U.S. corn market).
The degree of interdependence across exchanges has not necessarily
increased in recent years for all commodities.
The results provide additional information for policymakers should
they consider regulating futures markets.
E.g., a local regulatory initiative will probably have limited effects given
that agricultural exchanges are highly interrelated and there are volatility
spillovers.
Hernandez, Ibarra and Trupkin
Volatility transmission in agricultural futures markets
Thank you!