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- 저자 : Per A. Mykland (검색결과 2 건)
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An Asymptotic Decomposition of Hedging Errors
송성주,Per A. Mykland 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.2
This paper studies the problem of option hedging when the underlyingasset price process is a compound Poisson process. By adopting an asymp-totic approach to let the security price converge to a continuous process, wend a closed-form hedging strategy that improves the classical Black-Scholeshedging strategy in a quadratic sense. We rst show that the scaled Black-Scholes hedging error has a limit in law, and that limit is decomposed intoa part that can be traded away and a part that is purely unreplicable. TheBlack-Scholes hedging strategy is then modied by adding the replicablepart of its hedging error and by adding the mean-variance hedging strategyto the nonreplicable part. Some results of simulation experiments are alsoprovided.AMS 2000 subject classications.Primary 91B28; Secondary 60F05.Keywords.Hedging error, compound Poisson processes, weak convergence.1. IntroductionPerfect hedging of an option is impossible in the real world. In a completenancial market, every contingent claim is exactly attainable by investing inthe market. But in most real instances, the market is not complete. Underthe classical Black-Scholes setting, in which the stock price process is a geometricBrownian motion, we can construct a perfect hedging strategy because their setupassures that the market is complete. However, the stock price process is not ageometric Brownian motion and even not continuous in reality. Stocks move inxed increments that are multiples of the tick size and sometimes there are alsoReceived December 2005; accepted May 2006.1Corresponding author. Department of Statistics, Purdue University, West Lafayette, IN47909-2067, USA (e-mail: ssong@stat.purdue.edu)
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AN ASYMPTOTIC DECOMPOSITION OF HEDGING ERRORS
Song Seong-Joo,Mykland Per A. The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.2
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.
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