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Estimating Residual Hedging Risk With Least-Squares Monte Carlo

Author

Listed:
  • 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)

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.

Suggested Citation

  • Stefan Ankirchner & Christian Pigorsch & Nikolaus Schweizer, 2014. "Estimating Residual Hedging Risk With Least-Squares Monte Carlo," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-29.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:07:n:s0219024914500423
    DOI: 10.1142/S0219024914500423
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    References listed on IDEAS

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    1. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
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