PRICING ASIAN OPTIONS FOR JUMP DIFFUSION

Authors


  • We are grateful to the anonymous associate editor and two referees for detailed comments that helped us improve our paper. E. Bayraktar is supported in part by the National Science Foundation under an applied mathematics research grant and a Career grant, DMS-0906257and DMS-0955463, respectively, and in part by the Susan M. Smith Professorship.

Address correspondence to Erhan Bayraktar, Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109; e-mail: erhan@umich.edu.

Abstract

We construct a sequence of functions that uniformly converge (on compact sets) to the price of an Asian option, which is written on a stock whose dynamics follow a jump diffusion. The convergence is exponentially fast. We show that each element in this sequence is the unique classical solution of a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accuracy versus speed characteristics can be controlled. We analyze the performance of our numerical algorithm on several examples.

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