Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models
University of California, Santa Barbara
University of Toronto - Department of Statistics
ORFE Department, Pinceton University
August 2, 2010
SIAM Journal of Financial Mathematics, Forthcoming
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of European and path-dependent options in a fast mean-reverting stochastic volatility setting. Our method is shown to be equivalent to those developed in Fouque, Papanicolaou, and Sircar (2000), but has the advantage of being able to price options for which the methods of Fouque et.al. are unsuitable. In particular, we are able to price double-barrier options. To our knowledge, this is the first time that double-barrier options have been priced in a stochastic volatility setting in which the Brownian motions driving the stock and volatility are correlated.
Number of Pages in PDF File: 22
Keywords: Spectral Methods, Stochastic Volatility, Barrier OptionsAccepted Paper Series
Date posted: August 3, 2010 ; Last revised: June 29, 2011
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