Jump in Returns & Jump in Volatility

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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

Jump in Returns & Volatility

Jump in Returns & Jump in VolatilityKyu Won ChoiMarch 22, 2011+Data SetS&P 5001997/1/2 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) VIX2003/9/22 2008/12/31 (5-min prices)Though the same time period, inconsistent number of trading days (?)+OutlineFocus on Truncated Variance to detect the Jump in S&P 500 IndexJump 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 processContinuous processes Continuous + jump processesPure jump processes

Pure Jump Process from QASF, 5-min (Todorov, Tauchen 2010)

+Jump in Returns and VolatilityRealized Correlation between jumps in two series

T-statistics

+Realized Correlation

+16ProblemsIncorrect results because of the data/coding problem?Starting with 2003, the data clearingVIX data extra 11/28, 12/24, 12/26 (that SPFU does not have)Some days, missing the 5-min price data SPFUfixed 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)0.0~0.10.1~0.20.2~0.30.3~0.40.4~0.50.5~0.60.6~0.70.7~0.80.8~0.90.9~1.0135611117981

+T-statistics

+