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Formulating a Research Topic

Formulating a Research Topic. Abhinay Sawant February 18, 2009 Economics 201FS. Update from Last Time. Fixed programs: Z-Scores Tri-Power Quarticity Realized Volatility Signature Plots Still Coarse Sampling: Currently, sampling frequency = 8 min

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Formulating a Research Topic

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  1. Formulating a Research Topic Abhinay Sawant February 18, 2009 Economics 201FS

  2. Update from Last Time • Fixed programs: • Z-Scores • Tri-Power Quarticity • Realized Volatility Signature Plots • Still Coarse Sampling: • Currently, sampling frequency = 8 min • Should be changed to 5 minutes in future with averaging

  3. Homogeneity of Jumps

  4. Homogeneity of Jumps

  5. Homogeneity of Jumps • Let X1, X2, …, Xn be Bernoulli trials with probability p of success where success is defined as a jump day • Goal is to estimate p for pre-Lehman (1/1/06 – 9/12/08) and post-Lehman periods (9/15/08 – 1/7/09) • Conduct a t-Test to determine if a significance difference exists in parameter p in the two periods for individual equities

  6. Homogeneity of Jumps • Assume a prior distribution ξ(θ) uniformly distributed on the interval [0, 1] • Posterior distribution is a Beta distribution with the following parameters:

  7. Homogeneity of Jumps • Properties about estimated parameters can be determined as follows from Beta distribution: • t-Test is used to determine if difference is significant:

  8. Homogeneity of Jumps • Morgan Stanley (Tri-Power Quarticity): • Morgan Stanley (Quad-Power Quarticity):

  9. Homogeneity of Jumps • t Statistic measures the difference • Morgan Stanley t-Test: • Test is inconclusive but doesn’t suggest any significant difference in proportions

  10. Homogeneity of Jumps

  11. Homogeneity of Jumps

  12. Other Properties of Jumps

  13. Other Properties of Jumps • Morgan Stanley data:

  14. Other Properties of Jumps

  15. Alternative Research Topics Portfolio Risk • Constructing 2-asset portfolios and how does volatility change? • Realized Covariance: • How does investment process change for time-dependent volatility and correlation?

  16. Alternative Research Topics Risk Management • Incorporating time-dependent volatility for VaR model

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