Option Pricing with Mean Reversion and Stochastic Volatility
European Journal of Operational Research 197, 179-187, 2009
25 Pages Posted: 28 Mar 2008 Last revised: 13 Feb 2009
Date Written: January 23, 2008
Abstract
Many underlying assets of option contracts, such as currencies, commodities, energy, temperature and even some stocks, exhibit both mean reversion and stochastic volatility. This paper investigates the valuation of options when the underlying asset follows a mean-reverting lognormal process with stochastic volatility. A closed-form solution is derived for European options by means of Fourier transform. The proposed model allows the option pricing formula to capture both the term structure of futures prices and the market implied volatility smile within a unified framework. A bivariate trinomial lattice approach is introduced to value path-dependent options with the proposed model. Numerical examples using European options, American options and barrier options demonstrate the use of the model and the quality of the numerical scheme.
Keywords: Option Pricing, Mean Reversion, Stochastic Volatility
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