Bounds for the price of discrete arithmetic Asian options

Authors:
M. Vanmaele;G. Deelstra;J. Liinev;J. Dhaene;M. J. Goovaerts
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium;Department of Mathematics, ISRO and ECARES, Université Libre de Bruxelles, CP 210, 1050 Brussels, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium;Department of Applied Economics, Catholic University Leuven, Naamsestraat 69, 3000 Leuven, Belgium;Department of Applied Economics, Catholic University Leuven, Naamsestraat 69, 3000 Leuven, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random variables, as explained in Kaas et al. (Ins. Math. Econom. 27 (2000) 151-168), and additionally, the ideas of Rogers and Shi (J. Appl. Probab. 32 (1995) 1077-1088) and of Nielsen and Sandmann (J. Financial Quant. Anal. 38(2) (2003) 449-473). We are able to create a unifying framework for European-style discrete arithmetic Asian options through these bounds, that generalizes several approaches in the literature as well as improves the existing results. We obtain analytical and easily computable bounds. The aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters, investigate the effect of different conditioning variables and compare their efficiency numerically. Several sets of numerical results are included. We also discuss hedging using these bounds. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.