On the efficient application of the repeated Richardson extrapolation technique to option pricing
AbstractRichardson extrapolation (RE) is a commonly used technique in financial applications for accelerating the convergence of numerical methods. Particularly in option pricing, it is possible to refine the results of several approaches by applying RE, in order to avoid the difficulties of employing slowly converging schemes. But the effectiveness of such a technique is fully achieved when its repeated version (RRE) is applied. Nevertheless, its application in financial literature is pretty rare. This is probably due to the necessity to pay special attention to the numerical aspects of its implementation, such as the choice of both the sequence of the stepsizes and the order of the method. In this contribution, we consider several numerical schemes for the valuation of American options and investigate the possibility of an appropriate application of RRE. As a result, we find that, in the analyzed approaches in which the convergence is monotonic, RRE can be used as an effective tool for improving significantly the accuracy.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 147.
Length: 19 pages
Date of creation: Nov 2006
Date of revision:
Richardson extrapolation; repeated Richardson extrapolation; American options; randomization technique; flexible binomial method;
Find related papers by JEL classification:
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
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.:
- Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete-Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75.
- Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
- Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
- Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-46.
- Bunch, David S & Johnson, Herb, 1992. " A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-16, June.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco LiCalzi).
If references are entirely missing, you can add them using this form.