An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility
AbstractA 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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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 6867.
Date of creation: 21 Jan 2008
Date of revision:
Other versions of this item:
- Minqiang Li & Kyuseok Lee, 2011. "An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility," Quantitative Finance, Taylor and Francis Journals, vol. 11(8), pages 1245-1269.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-02-02 (All new papers)
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