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Analysis of Signature Volatility and Jump Detection in Financial Markets

This study analyzes signature volatility and jump detection in financial markets using raw data from Morgan Stanley and McDonald's Corp. It includes cleaning up raw data, plotting volatility, and identifying jump days at different significance levels.

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Analysis of Signature Volatility and Jump Detection in Financial Markets

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  1. Preliminary Data Analysis Abhinay Sawant February 4, 2009 Economics 201FS

  2. Raw Data • Morgan Stanley (MS): • January 17, 2009 – January 7, 2009 • 742 Days, 119 Imputed Data Points (0.04%) • McDonald’s Corp. (MCD): • April 17, 2009 – January 7, 2009 • 2,295 Days, 24,518 Imputed Data Points (2.18%) • Price data available every minute from 9:35 AM to 3:59 PM for each trading day

  3. Cleaning Up the Raw Data • McDonald's Corp. (MCD): • 2008-07-21: 3:58 pm 59.75 • 2008-07-21: 3:59 pm 59.79 • 2008-07-22: 9:35 am 0.001 • 2008-07-22: 9:36 am 0.001 • 2008-07-22: 9:37 am 59.995 • 2008-07-22: 9:38 am 60.058 • Imputed data for times 9:35 am and 9:36 am

  4. MS Share Price

  5. MCD Share Price

  6. MS Signature Volatility Plot • Not intraday returns, includes overnights

  7. MS Signature Volatility Plot • Not intraday returns, includes overnights

  8. MCD Signature Volatility Plot • Not intraday returns, includes overnights

  9. MCD Signature Volatility Plot • Not intraday returns, includes overnights

  10. MS Returns • Includes overnight returns

  11. MCD Returns • Includes overnight returns

  12. MS Realized Variance

  13. MCD Realized Variance

  14. MS Jump Detection: Quad-Power Quarticity • 1% Significance Level = 69 jump days / 742 (9.30%) • 5% Significance Level = 127 jump days / 742 (17.12%) • 10% Significance Level = 171 jump days / 742 (23.05%)

  15. MCD Jump Detection: Quad-Power Quarticity • 1% Significance Level = 458 jump days / 2925 (15.66%) • 5% Significance Level = 724 jump days / 2925 (24.75%) • 10% Significance Level = 859 jump days / 2925 (29.37%)

  16. MCD Jump Detection: Quad-Power Quarticity

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