Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models
Fouque, Jean-Pierre, Sebastian Jaimungal, and Matthew J. Lorig. "Spectral decomposition of option prices in fast mean-reverting stochastic volatility models." SIAM Journal on Financial Mathematics 2.1 (2011): 665-691.
22 Pages Posted: 3 Aug 2010 Last revised: 27 Apr 2015
Date Written: August 2, 2010
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.
Keywords: Spectral Methods, Stochastic Volatility, Barrier Options
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