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Numerical solution of generalized Black–Scholes model

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  • Chandra Sekhara Rao, S.
  • Manisha,

Abstract

This paper presents a numerical scheme that approximates the option prices for different option styles, governed by the generalized Black–Scholes equation in its degenerate form. The proposed method uses the HODIE scheme in the spacial direction and the two-step backward differentiation formula in the temporal direction. It is proved that the method has second order convergence in space as well as in time. Numerical experiments validate the theoretical results.

Suggested Citation

  • Chandra Sekhara Rao, S. & Manisha,, 2018. "Numerical solution of generalized Black–Scholes model," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 401-421.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:401-421
    DOI: 10.1016/j.amc.2017.10.004
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Hull, John & White, Alan, 1988. "The Use of the Control Variate Technique in Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(3), pages 237-251, September.
    3. Geske, Robert & Shastri, Kuldeep, 1985. "Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(1), pages 45-71, March.
    4. Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete‐Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75, January.
    5. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
    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. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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