An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility

Minqiang Li and Kyuseok Lee

Quantitative Finance, 2011, vol. 11, issue 8, 1245-1269

Abstract: A new successive over-relaxation method to compute the Black-Scholes implied volatility is introduced. Properties of the new method are fully analysed, 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.

Keywords: Successive over-relaxation; Black-Scholes formula; Implied volatility; Rational approximation (search for similar items in EconPapers)
Date: 2011
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Working Paper: An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility (2008)
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DOI: 10.1080/14697680902849361

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