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Probability and Computational Finance Seminar
Roger Lee Department of Mathematics University of Chicago Title: A Variance Contract is Worth How Many Log Contracts? Abstract: The standard variance swap theory (which underpins the VIX, VXN, and VSTOXX volatility indices) finds that a contract paying realized variance has the same value as 2 log contracts -- assuming continuous price paths. Introducing jump risk, we prove that a multiple of a log contract still prices a variance contract, under arbitrary exponential Levy dynamics, stochastically time-changed by an arbitrary integrable continuous clock, having arbitrary correlation with the driving Levy process. We solve for the multiplier, which depends only on the Levy process, not on the clock. In contrast to the 2 multiplier for the continuous case, we prove that the multiplier exceeds 2 in the presence of negatively skewed jump risk. We show moreover that discrete sampling increases variance swap values, under an independence condition; so if the commonly-quoted 2 multiple undervalues the continuously-sampled variance, then it undervalues furthermore the discretely-sampled variance. Joint with P Carr and L Wu. Date: Monday, March 22, 2010 Time: 5:00 pm Location: Wean Hall 6423 |