Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models
AbstractUsing 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 .  Jean-Pierre Fouque, George Papanicolaou, and Sircar Ronnie. Derivatives in Financial Markets with Stochas- tic Volatility. Cambridge University Press, 2000.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1007.4361.
Date of creation: Jul 2010
Date of revision: Apr 2012
Publication status: Published in SIAM J. Finan. Math. 2, (2011) pp. 665-691
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-08-06 (All new papers)
- NEP-ETS-2010-08-06 (Econometric Time Series)
- NEP-ORE-2010-08-06 (Operations Research)
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- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, July.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Antoon Pelsser, 2000. "Pricing double barrier options using Laplace transforms," Finance and Stochastics, Springer, vol. 4(1), pages 95-104.
- Eric Hillebrand, 2005. "Overlaying Time Scales in Financial Volatility Data," Econometrics 0501015, EconWPA.
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