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

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

2010-07-25

arxiv.org/abs/1007.4361v2

Economy

Quantitative Finance

Pricing of Securities

Scientific paper

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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