Jump in Returns & Jump in Volatility

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+ Jump in Returns & Jump in Volatility Kyu Won Choi March 22, 2011

description

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) - PowerPoint PPT Presentation

Transcript of Jump in Returns & Jump in Volatility

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Jump in Returns & Jump in Volatility

Kyu Won ChoiMarch 22, 2011

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+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 (?)

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+Outline

Focus on Truncated Variance to detect the Jump in S&P 500 Index

Jump in VIX using Power Variation

Realized Correlation & T-statistics

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+ S&P 500 Index

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+ Realized Variance & Bipower Variance

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+Realized Variance & Truncated (Threshold) Variance

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+ Truncated (Threshold) Variance3 SDs & 2SDs

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+ Jump Contribution (BV and 4ST TV)

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+ Jump Contribution(3SD and 2SD TV)

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+ VIX Index

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+ VIX: Power Variation (p = 2)

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+VIX : Power Variation (p=3,p=4)

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+VIX Power Variation (p=1, c=1,1.5)

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+ 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)

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+Jump in Returns and Volatility

Realized Correlation between jumps in two series

T-statistics

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+Realized Correlation

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+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?

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+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

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+ T-statistics