ADAPTIVE MESH MODELING AND BARRIER OPTION PRICING UNDER A JUMP-DIFFUSION PROCESS

The computational burden of numerical barrier option pricing is significant, even prohibitive, for some parameterizations-especially for more realistic models of underlying asset behavior, such as jump diffusions. We extend a binomial jump diffusion pricing algorithm into a trinomial setting and demonstrate how an adaptive mesh may fit into the model. Our result is a barrier option pricing method that employs fewer computational resources, reducing run times substantially. We demonstrate that this extension allows the pricing of options that were previously computationally infeasible and examine the parameterizations in which use of the adaptive mesh is most beneficial. (c) 2008 The Southern Finance Association and the Southwestern Finance Association.