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

See all articles by Jean-Pierre Fouque

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity

Sebastian Jaimungal

University of Toronto - Department of Statistics

Matthew Lorig

University of Washington - Applied Mathematics

Date Written: August 2, 2010

Abstract

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

Suggested Citation

Fouque, Jean-Pierre and Jaimungal, Sebastian and Lorig, Matthew, Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models (August 2, 2010). 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., Available at SSRN: https://ssrn.com/abstract=1652302

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity ( email )

United States

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Matthew Lorig

University of Washington - Applied Mathematics ( email )

Seattle, WA
United States

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