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

作者：Li Minqiang^*; Lee Kyuseok

来源：Quantitative Finance, 2011, 11(8): 1245-1269.

DOI：10.1080/14697680902849361

• Successive over-relaxation
• Black-Scholes formula
• Implied volatility
• Rational approximation

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.

• 出版日期2011