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Quasi Monte–Carlo Evaluation Of Sensitivities Of Options In Commodity And Energy Markets

Author

Listed:
  • FRED E. BENTH

    (Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N–0316 Oslo, Norway;
    Agder University College, Department of Economics and Business Administration, Serviceboks 422, N-4604 Kristiansand, Norway)

  • LARS O. DAHL

    (Storebrand Investments, P.O. Box 1380, N–0114 Oslo, Norway)

  • KENNETH H. KARLSEN

    (Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N–5008 Bergen, Norway;
    Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway)

Abstract

In this paper we consider the evaluation of sensitivities of options on spots and forward contracts in commodity and energy markets. We derive different expressions for these sensitivities, based on techniques from the recently introduced Malliavin approach [8, 9]. The Malliavin approach provides representations of the sensitivities in terms of expectations of the payoff and a random variable only depending on the underlying dynamics. We apply Monte–Carlo methods to evaluate such expectations, and to compare with numerical differentiation. We propose to use a refined quasi Monte–Carlo method based on adaptive techniques to reduce variance. Our approach gives a significant improvement of convergence.

Suggested Citation

  • Fred E. Benth & Lars O. Dahl & Kenneth H. Karlsen, 2003. "Quasi Monte–Carlo Evaluation Of Sensitivities Of Options In Commodity And Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(08), pages 865-884.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:08:n:s0219024903002250
    DOI: 10.1142/S0219024903002250
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