Volatility Spillovers Between Oil Prices And Stock Returns ...
A MEM-based Analysis of Volatility Spillovers in European Financial Markets
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A MEM-based Analysis of Volatility Spillovers in European Financial
Markets
Lena Golubovskaja
NUI Maynooth
FMC2/MACSI Colloquium
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Introduction
Theoretical Developments
The MEM Models
Empirical Results4
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Contents
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• Financial volatility has been extensively investigated for more than twenty-five years
• Financial integration => cross-country transmission mechanisms
• Strong empirical regularities about GARCH models
Analysis of Volatility
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Channels of Financial Contagion
Problems in a foreign bank subsidiary
Spillover to the parent
bank
Spillover to other countries where the parent banks and
other banks in home country have subsidiaries or engage in direct lending
to the private sector
Liquidity risk
Credit risk
Liquidity problems
Solvency problems
Spillover to other banks
in home country
Spillover to home banks with exposure to the affected subsidiary
Source: Árvai, Driessen, and Ötker-Robe (2009)
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Chou, Wu, and Yung (2010)
DJIA
SP500
NAS100
DAX30
FTSE100
CAC40
DJIA
SP500
NAS100
DAX30
FTSE100
CAC40
DJIA
SP500
NAS100
DAX30
FTSE100
CAC40
A: Entire Period B: Pre-subprime,
2001/02 – 2007/06
C: Post-subprime
2007/07 – 2010/01
The relationships between the U.S. and European Stock Price Ranges
?
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Whether volatility spillover effect exist between the European markets?
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Do we have a symmetric or assymetric volatility mechanism among the markets?
Who is the main volatility transmitter during the subprime mortgage crisis?
Hypothesis
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• Modelling non-negative time series– A lot of information available in financial
markets is positive valued: ultra-high frequency data (within a time interval: range, volume, number of trades, number of buys/sells, durations) daily volatility estimators (realized volatility, daily range, absolute returns)
– Time series exhibit persistence: GARCH–type models
Why Multiplicative Error Models?
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Germany: Daily Range, 1991-2011
Autocorrelation 0.737
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
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Range-based Volatility
Parkinson (1980) showed that that the range is an unbiased estimator of the volatility parameter in a diffusion process. The intuition behind his finding is that the price range of intraday gives more information regarding the future volatility than two arbitrary points in this series (the closing prices).
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Are These Days the Same?
Can we use this information to measure volatility better? Can we use this information to measure volatility better?
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Volatility Proxy
• The daily range
)log()log( ,, lowthightt PPhl
• Theoretical relative efficiency gain 2.5-5 (Parkinson, 1980)
• Directly observable from the data
• It is well approximated as Gaussian
• Robust to the microstructure noise (Brandt and Diebold, 2006)
22 ))2log(4/( dailyrangeE
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MEM
• Extension of GARCH approach to modelling the expected value of processes with positive support (Engle, 2002; Engle and Gallo, 2006)
• Autoregressive Conditional Duration is a special case
• Ease of estimation
• Possibility of expanding the information set
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The Base Model
Assumptions• a non-negative univariate process• the information about the process up to time t-1• MEM for is specified as
• is a nonnegative predictable process, depending on a vector of unknown parameters θ
• is a conditionally stochastic i.i.d. process, with density having non-negative support, mean 1 and unknown variance
thl
1tI
thltttt Ihl 1
t
).,1(~ 21 DI tt
t
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A Gamma Assumption for t
With and
/1)( 1 tt IV
)./1,(..~1 GammadiiI tt
11 tt I
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Gamma(4,1/4)
Chi-square
Gamma(2,1/2)
Exponential
=> )/,(~1 ttt GammaIhl
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Range Density
0.00 0.01 0.02 0.03 0.04 0.05 0.06
0
25
50
75
100
125
150
175
0.00 0.01 0.02 0.03 0.04 0.05
0
25
50
75
100
125
150
175
France
The Netherlands
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The specification of t
• Base(1,1) specification
1,1,, tiitiiiti hl
• Extended specification
1,01,1,,1,1,,
titiitjji
jitiitiiiti hlrIdhlhl
1, tir
0,0
0,10
1,
1,
1,ti
ti
ti rif
rifrI
- the return of stock i at time t-1.
- a dummy variable to test the leverage effect.
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Estimation
thl
)/(lnln)1()(lnlnln tttttt hlhlLl
• The contribution of to the log likelihood function is
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Gamma GED
• A useful relationship is between the Gamma distribution and the Generalized Error Distribution (GED):
• Thus the conditional density of hlt has a correspondence in a conditional density of hlt
where
).,,0(~)/,(~ 11 tttttt GEDHalfIhlGammaIhl
ttt vhl
).1,0(~1 NormalHalfIv tt
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Cross-autocorrelation matricesΥ0 hlFRA,t hlGER,t hlNETH,t hlSPA,t
hlFRA,t 1.000
hlGER,t 0.812 1.000
hlNETH,t 0.843 0.847 1.000
hlSPA,t 0.793 0.723 0.754 1.000
Υ1 hlFRA,t-1 hlGER,t-1 hlNETH,t-1 hlSPA,t-1
hlFRA,t 0.607 0.601 0.604 0.545
hlGER,t 0.597 0.737 0.660 0.545
hlNETH,t 0.599 0.671 0.695 0.552
hlSPA,t 0.559 0.564 0.564 0.625
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Estimation Results
t-stats
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Forecasting Performance
France Germany
SpainNetherlands
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
18/0
7/20
07
25/0
7/20
07
01/0
8/20
07
08/0
8/20
07
15/0
8/20
07
22/0
8/20
07
29/0
8/20
07
05/0
9/20
07
12/0
9/20
07
19/0
9/20
07
26/0
9/20
07
03/1
0/20
07
10/1
0/20
07
17/1
0/20
07
24/1
0/20
07
31/1
0/20
07
07/1
1/20
07
14/1
1/20
07
Forecast
Actual
0
0.01
0.02
0.03
0.04
0.05
0.06
18/0
7/20
07
25/0
7/20
07
01/0
8/20
07
08/0
8/20
07
15/0
8/20
07
22/0
8/20
07
29/0
8/20
07
05/0
9/20
07
12/0
9/20
07
19/0
9/20
07
26/0
9/20
07
03/1
0/20
07
10/1
0/20
07
17/1
0/20
07
24/1
0/20
07
31/1
0/20
07
07/1
1/20
07
14/1
1/20
07
Forecast
Actual
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
18/0
7/20
07
25/0
7/20
07
01/0
8/20
07
08/0
8/20
07
15/0
8/20
07
22/0
8/20
07
29/0
8/20
07
05/0
9/20
07
12/0
9/20
07
19/0
9/20
07
26/0
9/20
07
03/1
0/20
07
10/1
0/20
07
17/1
0/20
07
24/1
0/20
07
31/1
0/20
07
07/1
1/20
07
14/1
1/20
07
Forecast
Actual
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
18/0
7/2
007
25/0
7/2
007
01/0
8/2
007
08/0
8/2
007
15/0
8/2
007
22/0
8/2
007
29/0
8/2
007
05/0
9/2
007
12/0
9/2
007
19/0
9/2
007
26/0
9/2
007
03/1
0/2
007
10/1
0/2
007
17/1
0/2
007
24/1
0/2
007
31/1
0/2
007
07/1
1/2
007
14/1
1/2
007
Forecast
Actual
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Forecasting
Market France Germany Netherlands Spain
MEM MA(65) MEM MA(65) MEM MA(65) MEM MA(65)
ME -0.0006 -0.0008 -0.0004 -0.0007 -0.0004 -0.0011 -0.0001 -0.0010
MAE 0.0020 0.0023 0.0019 0.0021 0.0016 0.0021 0.0025 0.0029
RMSE 0.0027 0.0029 0.0025 0.0026 0.0021 0.0026 0.0033 0.0037
MSE 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
Theil’s U
0.7581 0.8036 0.7864 0.8027 0.8059 0.9802 0.7499 0.8309
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Summing Up
• We find evidence of dependence across European markets over full sample and over post-subprime
• MEM is a flexible class of models to estimate conditional expectations of non-negative processes
• Captures a wide range of features suggested by data structure
• Challenge: handle a large panel of data
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