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Removing the Correlation Term in Option Pricing Heston Model: Numerical Analysis and Computing

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  • R. Company
  • L. Jódar
  • M. Fakharany
  • M.-C. Casabán

Abstract

This paper deals with the numerical solution of option pricing stochastic volatility model described by a time‐dependent, two‐dimensional convection‐diffusion reaction equation. Firstly, the mixed spatial derivative of the partial differential equation (PDE) is removed by means of the classical technique for reduction of second‐order linear partial differential equations to canonical form. An explicit difference scheme with positive coefficients and only five‐point computational stencil is constructed. The boundary conditions are adapted to the boundaries of the rhomboid transformed numerical domain. Consistency of the scheme with the PDE is shown and stepsize discretization conditions in order to guarantee stability are established. Illustrative numerical examples are included.

Suggested Citation

  • R. Company & L. Jódar & M. Fakharany & M.-C. Casabán, 2013. "Removing the Correlation Term in Option Pricing Heston Model: Numerical Analysis and Computing," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:246724
    DOI: 10.1155/2013/246724
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    References listed on IDEAS

    as
    1. 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.
    2. Matthias Ehrhardt & Ronald E. Mickens, 2008. "A Fast, Stable And Accurate Numerical Method For The Black–Scholes Equation Of American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 471-501.
    3. 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.
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    Cited by:

    1. R. Company & V. N. Egorova & L. Jódar, 2016. "An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).

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