An Adaptive Successive Over-Relaxation Method for Computing the Black-Scholes Implied Volatility

57 Pages Posted: 15 Nov 2007

See all articles by Minqiang Li

Minqiang Li

Bloomberg LP

Kyuseok Lee

College of Business, Korea Advanced Institute of Science and Technology (KAIST)

Date Written: November 5, 2007

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 the well-definedness, and local and global convergence patterns. Quadratic order of convergence is achieved by either a transformation of sequence technique or dynamic relaxation. The method is further enhanced by introducing a rational approximation on initial values. Numerical implementation shows that uniformly in a very large approximation 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.

Keywords: Successive over-relaxation, Black-Scholes formula, Implied volatility, Convergence acceleration, Rational approximation

JEL Classification: C02, G13

Suggested Citation

Li, Minqiang and Lee, Kyuseok, An Adaptive Successive Over-Relaxation Method for Computing the Black-Scholes Implied Volatility (November 5, 2007). Available at SSRN: https://ssrn.com/abstract=1027282 or http://dx.doi.org/10.2139/ssrn.1027282

Minqiang Li (Contact Author)

Bloomberg LP ( email )

731 Lexington Avenue
New York, NY 10022
United States

Kyuseok Lee

College of Business, Korea Advanced Institute of Science and Technology (KAIST) ( email )

85 Hoegiro, Dongdaemoon-gu
Seoul 02455
Korea, Republic of (South Korea)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
670
Abstract Views
3,324
rank
39,409
PlumX Metrics