QUASI MONTE–CARLO EVALUATION OF SENSITIVITIES OF OPTIONS IN COMMODITY AND ENERGY MARKETS

Fred E. Benth (), Lars O. Dahl () and Kenneth H. Karlsen ()
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Fred E. Benth: Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N–0316 Oslo, 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;

International Journal of Theoretical and Applied Finance (IJTAF), 2003, vol. 06, issue 08, 865-884

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.

Keywords: Options; options in commodity and energy markets; sensitivity measures; hedging; Malliavin derivative; quasi Monte–Carlo simulation; adaptive methods (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0219024903002250

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