Li, Minqiang (2008): An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility.
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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|
|Original Title:||An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility|
|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
|Depositing User:||Minqiang Li|
|Date Deposited:||24. Jan 2008 05:37|
|Last Modified:||13. Feb 2013 12:58|