Abstract

https://ssrn.com/abstract=1797962
 


 



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


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; Das Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

March 28, 2011

Journal of Derivatives, Vol. 20, No. 3, 2013

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


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Date posted: March 30, 2011 ; Last revised: June 20, 2014

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

Contact Information

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
Das Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM ( email )
Fraunhofer-Platz 1
Kaiserslautern, 67663
Germany
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