Estimating Residual Hedging Risk with Least-Squares Monte Carlo

30 Pages Posted: 30 Oct 2012 Last revised: 6 Mar 2013

See all articles by Stefan Ankirchner

Stefan Ankirchner

University of Bonn

Christian Pigorsch

Ludwig Maximilian University of Munich (LMU) - Department of Statistics

Nikolaus Schweizer

Tilburg School of Economics and Management

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

Suggested Citation

Ankirchner, Stefan and Pigorsch, Christian and Schweizer, Nikolaus, Estimating Residual Hedging Risk with Least-Squares Monte Carlo (September 3, 2012). Available at SSRN: https://ssrn.com/abstract=2168847 or http://dx.doi.org/10.2139/ssrn.2168847

Stefan Ankirchner

University of Bonn ( email )

Regina-Pacis-Weg 3
Postfach 2220
Bonn, D-53012
Germany

Christian Pigorsch

Ludwig Maximilian University of Munich (LMU) - Department of Statistics ( email )

Ludwigstr. 33
Munchen, D-80539
Germany

Nikolaus Schweizer (Contact Author)

Tilburg School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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