Jumps in High Volatility Environments and Extreme Value Theory
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Transcript Jumps in High Volatility Environments and Extreme Value Theory
Jumps in High Volatility Environments
and Extreme Value Theory
Abhinay Sawant
March 4, 2009
Economics 201FS
Overview
Jumps in High Volatility Last Environment: Updated method from
previous time
Extreme Value Theory: Read current literature on topic but haven’t
decided how to apply it to data
Set-Up of Test
Pre-Lehman Period: All data through September 12, 2008
Post-Lehman Period: September 15, 2008 – January 4, 2009 (78 days)
Difference of Sample Means t Test:
t
X 2 X1
s12 s22
n1 n2
Assumption: t distribution is approximately normal for high sample size
Results: Financial Stocks
Company Name
zQP
zTP
Bank of America (BAC)
1.631
1.669
Bank of New York (BK)
–0.483
-0.578
0.354
0.459
Capital One Financial (COF)
-0.603
0.426
Goldman Sachs (GS)
-0.633
-0.568
1.727
1.748
-0.255
-0.319
Regions Financial Corp. (RF)
1.650
1.653
U.S. Bancorp (USB)
0.055
0.048
Wells Fargo (WFC)
0.944
1.012
Citigroup (C)
JPMorgan Chase (JPM)
Morgan Stanley (MS)
Results: Non-Financial Stocks
Company Name
zQP
zTP
Cisco (CSCO)
-1.875
-1.797
Intel (INTC)
-1.472
-1.476
Hewlett-Packard (HPQ)
-1.547
-1.477
Pfizer (PFE)
-0.053
0.015
Merck (MRK)
-0.086
-0.065
Johnson & Johnson (JNJ)
-0.161
-0.222
Wal-Mart (WMT)
-2.193
-2.070
Procter & Gamble (PG)
0.734
0.865
PepsiCo (PEP)
0.051
0.096
Lockheed Martin (LMT)
-0.860
-0.720
Caterpillar (CAT)
-4.385
-4.246
Honeywell (HON)
-2.991
-2.760
Jumps in High Volatility Environments
Regression of Realized Volatility on Z-Scores
Comparisons across Industries
Extreme Value Theory
Extreme Value Theory
Extreme Value Theory: Background Theory
General Pareto Distribution (GPD) describes values of x above the
threshold u:
F ( x | x u) 1 1 ( x u)
1
0
ξ and β are to be estimated using Maximum Likelihood Estimation
Hill’s Estimator:
1 k 1
ln X i ,n ln X k ,n
k 1 i 1
Extreme Value Theory: Background Theory
Extreme Value Theory allows for the estimation of risk metrics:
n
VaRp u
p 1
Nu
VaRp ˆ u
ES p
1
1 ˆ
Extreme Value Theory: Current Literature
High-frequency tail estimation has efficiency benefits since intraday
data allows for observable extremes (Cotter and Longin, 2004)
Margin setting based on closing prices alone underestimates the
risk, when compared with intraday data (Cotter and Longin, 2004)
High-frequency volatility estimator based on EVT provides superior
forecasting abilities when compared to GARCH discrete time
models (Bali and Weinbaum, 2006)
Further Direction
Does the financial crisis period offer extreme values of returns and
can GPD model adequately estimate these values of returns?
At high frequency, do the extreme intraday returns represent jumps
or rapid movement in prices?