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Pricing American options in the Heston model: a close look on incorporating correlation

  • 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 tree moments up to order two against the Heston model ones. The correlation between the driving Brownian motions in the Heston model is then incorporated by the 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 dis- cretization 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.

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Author:P. Ruckdeschel, T. Sayer, A. Szimayer
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16957
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (204)
Document Type:Report
Language of publication:English
Year of Completion:2011
Year of Publication:2011
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2011/04/26
GND-Keyword:American options; Heston model; corre- lation; moment matching; tree method
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011