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An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility

Author

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  • Li, Minqiang

Abstract

A new successive over-relaxation method to compute the Black-Scholes implied volatility is introduced. Properties of the new method are fully analyzed, including global well-definedness, local convergence, as well as global convergence. Quadratic order of convergence is achieved by either a dynamic relaxation or transformation of sequence technique. The method is further enhanced by introducing a rational approximation on initial values. Numerical implementation shows that uniformly in a very large domain, the new method converges to the true implied volatility with very few iterations. Overall, the new method achieves a very good combination of efficiency, accuracy and robustness.

Suggested Citation

  • Li, Minqiang, 2008. "An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility," MPRA Paper 6867, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:6867
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    File URL: https://mpra.ub.uni-muenchen.de/6867/1/MPRA_paper_6867.pdf
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    References listed on IDEAS

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    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    2. 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.
    3. Chance, Don M, 1996. "A Generalized Simple Formula to Compute the Implied Volatility," The Financial Review, Eastern Finance Association, vol. 31(4), pages 859-867, November.
    4. Corrado, Charles J. & Miller, Thomas Jr., 1996. "A note on a simple, accurate formula to compute implied standard deviations," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 595-603, April.
    5. Chambers, Donald R & Nawalkha, Sanjay K, 2001. "An Improved Approach to Computing Implied Volatility," The Financial Review, Eastern Finance Association, vol. 36(3), pages 89-99, August.
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    Cited by:

    1. repec:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500480 is not listed on IDEAS
    2. Liu, Yi-Fang & Zhang, Wei & Xu, Hai-Chuan, 2014. "Collective behavior and options volatility smile: An agent-based explanation," Economic Modelling, Elsevier, vol. 39(C), pages 232-239.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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