Pricing American Options under Stochastic Volatility and Stochastic Interest Rates

34 Pages Posted: 1 Mar 2007 Last revised: 21 Sep 2009

See all articles by Alexey Medvedev

Alexey Medvedev

Lombard Odier & Cie

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics

Date Written: September 1, 2009

Abstract

We introduce a new analytical approach to price American options. Using an explicit and intuitive proxy for the exercise rule, we derive tractable pricing formulas using a short-maturity asymptotic expansion. Depending on model parameters, this method can accurately price options with time-to-maturity up to several years. The main advantage of our approach over existing methods lies in its straightforward extension to models with stochastic volatility and stochastic interest rates. We exploit this advantage by providing an analysis of the impact of volatility mean-reversion, volatility of volatility, and correlations on the American put price.

Keywords: American options, stochastic volatility, stochastic interest rates, asymptotic approximation.

JEL Classification: G12

Suggested Citation

Medvedev, Alexey and Scaillet, Olivier, Pricing American Options under Stochastic Volatility and Stochastic Interest Rates (September 1, 2009). Swiss Finance Institute Research Paper No. 07-25. Available at SSRN: https://ssrn.com/abstract=966055 or http://dx.doi.org/10.2139/ssrn.966055

Alexey Medvedev (Contact Author)

Lombard Odier & Cie ( email )

11 rue de la Corraterie
1211 Geneva 11
Switzerland

Olivier Scaillet

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland
+ 41 22 379 88 16 (Phone)
+41 22 389 81 04 (Fax)

HOME PAGE: http://www.scaillet.ch

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva - Research Center for Statistics

Geneva
Switzerland

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