The Valuation of Structured Products Using Markov Chain Models

24 Pages Posted: 4 Mar 2010 Last revised: 14 May 2011

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Martijn Pistorius

Imperial College London

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: March 2, 2010

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

Suggested Citation

Madan, Dilip B. and Pistorius, Martijn and Schoutens, Wim, The Valuation of Structured Products Using Markov Chain Models (March 2, 2010). Robert H. Smith School Research Paper No. RHS 06-142, Available at SSRN: https://ssrn.com/abstract=1563500 or http://dx.doi.org/10.2139/ssrn.1563500

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Martijn Pistorius

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/m.pistorius

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium