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arXiv · 1007.4361

Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models

Jean-Pierre Fouque·Sebastian Jaimungal·Matthew Lorig
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Abstract

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European options, up-and-out options, double-barrier knock-out options, and options which pay a rebate upon hitting a boundary. For European options, our method is shown to produce option price approximations which are equivalent to those developed in [5]. [5] Jean-Pierre Fouque, George Papanicolaou, and Sircar Ronnie. Derivatives in Financial Markets with Stochas- tic Volatility. Cambridge University Press, 2000.

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Jean-Pierre Fouque, Sebastian Jaimungal, Matthew Lorig. 2010-07-25. Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models. https://doi.org/10.1137/100803614

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