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Efficient Discrete Time Jump Process Models in Option Pricing

Published online by Cambridge University Press:  06 April 2009

Edward Omberg
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Abstract

A family of jump process models is derived by applying Gauss-Hermite quadrature to the recursive integration problem presented by a compound option model. The result is jump processes of any order with known efficiency properties in valuing options. In addition, these processes arise in the replication of options over finite periods of time with two or more assets where they again have known efficiency properties. A “sharpened” trinomial process is designed that accounts for the first-derivative discontinuity in option valuation functions at critical exercise points. It is shown to have accuracy superior to that of conventional binomial and trinomial processes and is nearly identical to the trinomial process optimized by Boyle (1988) through trial and error.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 23 , Issue 2 , June 1988 , pp. 161 - 174
Copyright
Copyright © School of Business Administration, University of Washington 1988

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