Pricing Discrete Barrier Options with an Adaptive Mesh Model

Abstract

The binomial option pricing model and the trinomial model, its more versatile relative, are invaluable tools for pricing complex derivatives, especially those with American exercise. But while these models converge to the correct option values as the time and price step sizes go to zero, for certain kinds of problems getting close enough may require a very large amount of calculation. The cause is often non-linearity or discontinuity in the option payoff that occurs only in a small region. One example is a barrier option with a barrier that is only monitored at discrete intervals. This article describes how to solve the discrete barrier problem with an adaptive mesh model, a general approach to lattice building that constructs smell sections of fine high-resolution mesh in the critical areas and then grafts them onto a base lattice with coarser time and price steps elsewhere. The technique achieves an increase in accuracy that is quite remarkable.