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

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  • Jean-Pierre Fouque
  • Sebastian Jaimungal
  • Matthew Lorig
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    Abstract

    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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    File URL: http://arxiv.org/pdf/1007.4361
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1007.4361.

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    Date of creation: Jul 2010
    Date of revision: Apr 2012
    Publication status: Published in SIAM J. Finan. Math. 2, (2011) pp. 665-691
    Handle: RePEc:arx:papers:1007.4361

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    Web page: http://arxiv.org/

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    1. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, July.
    2. 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.
    3. Antoon Pelsser, 2000. "Pricing double barrier options using Laplace transforms," Finance and Stochastics, Springer, vol. 4(1), pages 95-104.
    4. Eric Hillebrand, 2005. "Overlaying Time Scales in Financial Volatility Data," Econometrics 0501015, EconWPA.
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