A Lattice Approach to Pricing of Multivariate Contingent Claims with Regime Switching

Abstract

One of the most challenging areas in derivatives valuation is pricing securities whose payoffs depend on multiple underlying assets, such as a “best of N” rainbow option. Incorporating real-world features, such as correlation in the underlying stochastic processes and high- and low-volatility regimes for individual assets, is the kind of problem that has required intensive and very time-consuming Monte Carlo simulation in order to achieve a reasonable level of accuracy. Lattice models have been developed for correlated processes, but not with possible jumps among multiple regimes. This article presents such a model. Not surprisingly, it is quite complicated and challenges the reader’s spacial intuition, but the end result is a lattice framework that covers multiple assets following correlated diffusions at every point in time, each of which can also experience jumps among alternative regimes. Accurate pricing is achieved in the lattice in much shorter time than is possible with Monte Carlo methods.