Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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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)
  • Published : 2006.06.01
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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

References

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