An Adaptive Succesive Over-relaxation Method for Computing the Black-Scholes Implied Volatility
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.
|Date of creation:||21 Jan 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chambers, Donald R & Nawalkha, Sanjay K, 2001. "An Improved Approach to Computing Implied Volatility," The Financial Review, Eastern Finance Association, vol. 36(3), pages 89-99, August.
- Peter Carr & Liuren Wu, 2003.
"The Finite Moment Log Stable Process and Option Pricing,"
Journal of Finance,
American Finance Association, vol. 58(2), pages 753-778, 04.
- Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Corrado, Charles J. & Miller, Thomas Jr., 1996. "A note on a simple, accurate formula to compute implied standard deviations," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 595-603, April.
- Chance, Don M, 1996. "A Generalized Simple Formula to Compute the Implied Volatility," The Financial Review, Eastern Finance Association, vol. 31(4), pages 859-67, November.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:6867. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)
If references are entirely missing, you can add them using this form.