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

Li, Minqiang (2008): An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility.

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.

• Item Type: MPRA Paper
• Language: English
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing