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Pricing Parisian Option under a Stochastic Volatility Model

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  • Min-Ku Lee
  • Kyu-Hwan Jang

Abstract

We study the pricing of a Parisian option under a stochastic volatility model. Based on the manipulation problem that barrier options might create near barriers, the Parisian option has been designed as an extended barrier option. A stochastic volatility correction to the Black‐Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically.

Suggested Citation

  • Min-Ku Lee & Kyu-Hwan Jang, 2014. "Pricing Parisian Option under a Stochastic Volatility Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:956454
    DOI: 10.1155/2014/956454
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    References listed on IDEAS

    as
    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, August.
    2. Céline Labart & Jérôme Lelong, 2009. "Pricing Parisian options using Laplace transforms," Post-Print hal-00776703, HAL.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    5. Céline Labart & Jérôme Lelong, 2009. "Pricing Double Barrier Parisian Options Using Laplace Transforms," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 19-44.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Zhu, Song-Ping & Chen, Wen-Ting, 2013. "Pricing Parisian and Parasian options analytically," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 875-896.
    8. repec:dau:papers:123456789/1392 is not listed on IDEAS
    9. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
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