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Pricing American Options in the Heston Model: A Close Look on Incorporating Correlation

Posted: 30 Mar 2011 Last revised: 20 Jun 2014

Peter Ruckdeschel

University of Oldenburg - School of Mathematics and Science

Tilman Sayer

Advanced Logic Analytics

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration

Date Written: March 28, 2011

Abstract

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

Suggested Citation

Ruckdeschel, Peter and Sayer, Tilman and Szimayer, Alexander, Pricing American Options in the Heston Model: A Close Look on Incorporating Correlation (March 28, 2011). Journal of Derivatives, Vol. 20, No. 3, 2013 . Available at SSRN: https://ssrn.com/abstract=1797962 or http://dx.doi.org/10.2139/ssrn.1797962

Peter Ruckdeschel

University of Oldenburg - School of Mathematics and Science ( email )

PO box 2503
Oldenburg, 26111
Germany

Tilman Sayer (Contact Author)

Advanced Logic Analytics

London
United Kingdom

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

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