Estimating Residual Hedging Risk with Least-Squares Monte Carlo
30 Pages Posted: 30 Oct 2012 Last revised: 6 Mar 2013
Date Written: September 3, 2012
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: basis risk, cross-hedging, hedging error, incomplete markets, least-squares Monte Carlo
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