Articlegreen2008

FOREIGN EXCHANGE OPTIONS UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES

25 citations0/0 files storedInternational Journal of Theoretical and Applied Finance

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Risk Management in Financial Firms

Abstract

In this paper, we present a stochastic volatility model with stochastic interest rates in a Foreign Exchange (FX) setting. The instantaneous volatility follows a mean-reverting Ornstein–Uhlenbeck process and is correlated with the exchange rate. The domestic and foreign interest rates are modeled by mean-reverting Ornstein–Uhlenbeck processes. The main result is an analytic formula for the price of a European call on the exchange rate. It is derived using martingale methods in arbitrage pricing of contingent claims and Fourier inversion techniques.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 1973Theory of Rational Option Pricing 2005Theory of rational option pricing 1977An equilibrium characterization of the term structure 1976Option pricing when underlying stock returns are discontinuous 1987The Pricing of Options on Assets with Stochastic Volatilities

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