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Department of Statistics, University of Chicago

Mathematical Finance,Vol. 15, No. 2 (April 2005), 309 343 EVALUATING HEDGING ERRORS: AN ASYMPTOTIC APPROACHTAKAKIHAYASHID epartment of statistics , Columbia UniversityPERA. MYKLANDD epartment of statistics , University of ChicagoWepropose a methodology for evaluating the hedging errors of derivative securitiesdue to the discreteness of trading times or the observation times of market prices, orboth. Utilizing a weak convergence approach, we derive the asymptotic distributions ofthe hedging errors as the discreteness disappears in several situations. First, we examinethe hedging error due to discrete-time trading when the true strategy is known, whichgeneralizes the result of Bertsimas, Kogan, and Lo (2000) to continuous It we consider a data-driven strategy, when the true strategy is unknown. Thisstrategy is free of parametric model assumptions, therefore it is expected to serve asabenchmark for the evaluation of parametric strategies.

Department of Statistics, Columbia University PER A. MYKLAND Department of Statistics, University of Chicago We propose a methodology for evaluating the hedging errors of derivative securities due to the discreteness of trading times or the observation times of market prices, or

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