jump in returns & jump in volatility

+

Jump in Returns & Jump in Volatility

Kyu Won ChoiMarch 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) Variance3 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

0.1~0.2

0.2~0.3

0.3~0.4

0.4~0.5

0.5~0.6

0.6~0.7

0.7~0.8

0.8~0.9

0.9~1.0

1 3 5 6 11 11 7 9 8 1

+ T-statistics