| Purdue Computational Finance Program | |
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Evaluating Hedging Errors: An Asymptotic Approach
January 31, 2003 |
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Abstract:
We propose a methodology for evaluating the hedging errors of contingent claims due to the discreteness of trading times and/or observation times of market prices. Utilizing a weak convergence approach, we derive the asymptotic distributions of the hedging errors as the discreteness disappears in several situations. First, we examine the hedging error due to discrete-time trading when the true strategy is known, which generalizes the result of Bertsimas, Kogan, and Lo (2000) to continuous Ito processes. Then, we consider a data-driven strategy, when the true strategy is unknown. This strategy is free of parametric model assumptions, thus it is expected to serve as a benchmark for the evaluation of parametric strategies. Finally, we investigate the Black-Scholes delta-hedging strategy with the implied volatility when the volatility is unknown. The results show the efficacy of our approach which covers broad and important classes of models, giving us a prospect for the further development of the framework under which various parametric strategies could be compared in a unified manner. |
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2003 Purdue University Last Update: Jan 31, 2003 Please send comments and suggestions to the Webmaster. |