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Applied Math Seminar
Robust Hedging of Volatility Derivatives: Recent Progress
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Define the realized variance of a price process S to be the quadratic variation of log(S) from time 0 to time T. (In practice, Wall Street dealers in variance contracts typically use the sample variance of the daily or weekly returns of S.) By trading S and European options on S, we replicate derivative contracts which pay out general functions of realized variance, such as its square root, realized volatility. Unlike previous efforts to hedge general volatility derivatives, we avoid imposing any specific volatility model on the S diffusion. We make only a correlation assumption. This talk, while self-contained, will emphasize recent progress in: 1. Relaxation of the correlation assumption 2. Discrete approximation of the pricing/hedging problem, and solution via regularization methods for inverse problems 3. Extension to jump-diffusions This work is joint with Peter Carr. |