The Valuation of Structured Products Using Markov Chain Models

Abstract

A Markov chain with an expanding non-uniform grid matching risk neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with prespecified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from option data. For Markov chains dynamically consistent sequences of bid and ask prices are developed by applying the theory of nonlinear expectations with drivers given by concave distortions applied to the one step ahead risk.The procedures are illustrated by generating dynamically consistent bid ask sequences for a variety of structured products, like locally capped and floored cliquets, rolling calls and puts and hedged and unhedged variance swap contracts. Two sided nonlinear barrier pricing of straddles is also accomplished. All methods are illustrated on the surface of JPM on October 15 2009.

Keywords: Variance Gamma, Local Levy, Barrier Pricing, Sato Process

JEL Classification: G10, G11, G12