ESTIMATING RESIDUAL HEDGING RISK WITH LEAST-SQUARES MONTE CARLO

Stefan Ankirchner (), Christian Pigorsch () and Nikolaus Schweizer ()
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Stefan Ankirchner: Institute for Mathematics, University of Jena, 07743 Jena, Ernst-Abbe-Platz 2, Germany
Christian Pigorsch: Faculty of Economics and Business Administration, University of Jena, 07743 Jena, Carl-Zeiß-Straße 3, Germany
Nikolaus Schweizer: Mercator School of Management, University of Duisburg-Essen, 47057 Duisburg, Lotharstraße 65, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 07, 1-29

Abstract: Frequently, dynamic hedging strategies minimizing risk exposure are not given in closed form, but need to be approximated numerically. This makes it difficult to estimate residual hedging risk, also called basis risk, when only imperfect hedging instruments are at hand. We propose an easy to implement and computationally efficient least-squares Monte Carlo algorithm to estimate residual hedging risk. The algorithm approximates the variance minimal hedging strategy within general diffusion models. Moreover, the algorithm produces both high-biased and low-biased estimators for the residual hedging error variance, thus providing an intrinsic criterion for the quality of the approximation. In a number of examples we show that the algorithm delivers accurate hedging error characteristics within seconds.

Keywords: Hedging risk; variance bounds; least-squares Monte Carlo (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219024914500423

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