Primal and Dual Pricing of Multiple Exercise Options in Continuous Time

Abstract

In this paper we study the pricing problem of multiple exercise options in continuous time on a finite time horizon. For the corresponding multiple stopping problem, we prove, under quite general assumptions, the existence of the Snell envelope, a reduction principle as nested single stopping problems, and a Doob–Meyer-type decomposition for the Snell envelope. The main technical difficulty arises from the fact that the price process of a multiple exercise option typically exhibits discontinuities from the right-hand side, even if the payoff process of the option is right-continuous. We also derive a dual minimization problem for the price of the multiple exercise option in terms of martingales and processes of bounded variation. Moreover, we explain how the primal and dual pricing formulas can be applied to compute confidence intervals on the option price via Monte Carlo methods, and we present a numerical example.

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