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Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models

Author

Listed:
  • M.-C. Casabán
  • R. Company
  • L. Jódar
  • J.-V. Romero

Abstract

A new discretization strategy is introduced for the numerical solution of partial integrodifferential equations appearing in option pricing jump diffusion models. In order to consider the unknown behaviour of the solution in the unbounded part of the spatial domain, a double discretization is proposed. Stability, consistency, and positivity of the resulting explicit scheme are analyzed. Advantages of the method are illustrated with several examples.

Suggested Citation

  • M.-C. Casabán & R. Company & L. Jódar & J.-V. Romero, 2012. "Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:120358
    DOI: 10.1155/2012/120358
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    References listed on IDEAS

    as
    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    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. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    5. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    6. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.
    7. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    8. 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.
    9. A. -M. Matache & P. -A. Nitsche & C. Schwab, 2005. "Wavelet Galerkin pricing of American options on Levy driven assets," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 403-424.
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    Cited by:

    1. R. Company & L. Jódar & M. Fakharany, 2013. "Positive Solutions of European Option Pricing with CGMY Process Models Using Double Discretization Difference Schemes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. M. Fakharany & R. Company & L. Jódar, 2015. "Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).

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