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AN ASYMPTOTIC DECOMPOSITION OF HEDGING ERRORS  

Song Seong-Joo (Department of Statistics, Purdue University)
Mykland Per A. (Department of Statistics, The University of Chicago)
Publication Information
Journal of the Korean Statistical Society / v.35, no.2, 2006 , pp. 115-142 More about this Journal
Abstract
This paper studies the problem of option hedging when the underlying asset price process is a compound Poisson process. By adopting an asymptotic approach to let the security price converge to a continuous process, we find a closed-form hedging strategy that improves the classical Black-Scholes hedging strategy in a quadratic sense. We first show that the scaled Black-scholes hedging error has a limit in law, and that limit is decomposed into a part that can be traded away and a part that is purely unreplicable. The Black-Scholes hedging strategy is then modified by adding the replicable part of its hedging error and by adding the mean-variance hedging strategy to the nonreplicable part. Some results of simulation experiment s are also provided.
Keywords
Hedging error; compound Poisson processes; weak convergence;
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