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

Swiss Finance Institute - University of Geneva

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 )

Avenue des Morgines 6
Petit-Lancy
Switzerland

Olivier Scaillet

Swiss Finance Institute - University of Geneva ( email )

Geneva
Switzerland

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