Pricing Parisian Options

In this article, we present a flexible approach to the valuation of Parisian and similar exotic options. The approach is based on the numerical solution of a fundamental partial differential equation and can easily accommodate variations like American early exercise features, different payoff functions, or differences in the way of counting the barrier time. In the first part of the article, the state space, the dynamics of the state variables, and the fundamental pricing equations are introduced. Next we show how to modify the approach for variations of the basic Parisian option, and give a numerical implementation scheme for the solution of the option pricing problem. Finally, some characteristic features of the pricing and hedging of Parisian options are discussed, using the results of the numerical scheme.