Download Talk1

+
Jump in Returns
& Jump in Volatility
Kyu Won Choi
March 22, 2011
+
Data Set

S&P 500

1997/1/2 – 2010/12/30 (3482 trading days)

1-min frequency prices from 9:35am to 3:59pm

Extracted prices from 2003/9/22 to 2008/12/31 (1316 trading
days)


For 5-min RV & BV & TV (jump detection) alone (76 returns per
day)
VIX

2003/9/22 – 2008/12/31 (5-min prices)

Though the same time period, inconsistent number of trading
days (?)
+
Outline

Focus on Truncated Variance to detect the Jump in S&P 500 Index

Jump in VIX using Power Variation

Realized Correlation & T-statistics
+
S&P 500 Index
+
Realized Variance &
Bipower Variance
+
Realized Variance &
Truncated (Threshold) Variance
+
Truncated (Threshold) Variance
3 SDs & 2SDs
+
Jump Contribution
(BV and 4ST TV)
+
Jump Contribution
(3SD and 2SD TV)
+
VIX Index
+
VIX: Power Variation (p = 2)
+
VIX : Power Variation (p=3,p=4)
+
VIX Power Variation (p=1, c=1,1.5)
+
Activity Index
(Todorov, Tauchen 2010)

Activity Signature Function (ASF) behaves differently for the
process

Continuous processes

Continuous + jump processes

Pure jump processes

Pure Jump Process from
QASF, 5-min (Todorov, Tauchen 2010)
+
Jump in Returns and Volatility

Realized Correlation between jumps in two series

T-statistics
+
Realized Correlation
+
Problems

Incorrect results because of the data/coding problem?

Starting with 2003, the data clearing


VIX data

extra 11/28, 12/24, 12/26 (that SPFU does not have)

Some days, missing the 5-min price data
SPFU


fixed closing price: 5-minute frequency (to be consistent )
Analyze the results year by year

During the times of market stress, is the correlation between jump
in price and volatility higher than other times?
+
Realized Correlation (2003)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
~0.1 ~0.2 ~0.3 ~0.4 ~0.5 ~0.6 ~0.7 ~0.8 ~0.9 ~1.0
1
3
5
6
11
11
7
9
8
1
+
T-statistics