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

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6867.

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Date of creation: 21 Jan 2008
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Handle: RePEc:pra:mprapa:6867

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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, American Finance Association, vol. 58(2), pages 753-778, 04.
  2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  3. Corrado, Charles J. & Miller, Thomas Jr., 1996. "A note on a simple, accurate formula to compute implied standard deviations," Journal of Banking & Finance, Elsevier, Elsevier, vol. 20(3), pages 595-603, April.
  4. Chambers, Donald R & Nawalkha, Sanjay K, 2001. "An Improved Approach to Computing Implied Volatility," The Financial Review, Eastern Finance Association, Eastern Finance Association, vol. 36(3), pages 89-99, August.
  5. Chance, Don M, 1996. "A Generalized Simple Formula to Compute the Implied Volatility," The Financial Review, Eastern Finance Association, Eastern Finance Association, vol. 31(4), pages 859-67, November.
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