Pricing lookback strike put options with barrier by partial differential equation approach

Abstract

We consider the problem of pricing lookback option with barrier whose payoff depends on the maximal stock price as well as the terminal price during the contract period. In addition the option becomes void when the stock price crosses an upper bound. We first reduce the problem to an partial differential equation with both Dirichlet and Robin boundary conditions. An explicit pricing formula is then obtained by finding an appropriate Green's function and applying Laplace transform. Approaches developed here can be easily applied to pricing other types of lookback options with barrier.