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Li, Minqiang; Lee, Kyuseok

An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility. (English) Zbl 1266.91118

Quant. Finance 11, No. 8, 1245-1269 (2011).
Summary: 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.

Cited in 5 Documents

MSC:

91G60 Numerical methods (including Monte Carlo methods)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

successive over-relaxation; Black-Scholes formula; implied volatility; rational approximation
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