Pricing American Options in the Heston Model: A Close Look on Incorporating Correlation
University of Oldenburg - School of Mathematics and Science; Fraunhofer ITWM
Department of Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM
University of Hamburg - Faculty of Economics and Business Administration; Das Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM
March 28, 2011
Journal of Derivatives, Vol. 20, No. 3, 2013
We introduce a refined tree method to compute option prices using the stochastic volatility model of Heston. In a first step, we model the stock and variance process as two separate trees and with transition probabilities obtained by matching marginal tree moments up to order two against the Heston model ones. The correlation between the driving Brownian motions is then incorporated by a node-wise adjustment of the probabilities. This adjustment, leaving the marginals fixed, optimizes the match between tree and model correlation. In some nodes, we are even able to further match moments of higher order. Numerically this gives convergence orders faster than 1/N, where N is the number of discretization steps. Accuracy of our method is checked for European option prices against a semi closed-form, and our prices for both European and American options are compared to alternative approaches.
Keywords: Heston Model, American Options, Moment Matching, Correlation, Tree Method
JEL Classification: C00, G12, G13
Date posted: March 30, 2011 ; Last revised: June 20, 2014
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