Richardson Extrapolation Techniques for the Pricing of American-Style Options

26 Pages Posted: 12 Jun 2002

See all articles by San-Lin Chung

San-Lin Chung

National Central University at Taiwan - Department of Finance

Chuang-Chang Chang

National Central University at Taiwan - Department of Finance

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance

Date Written: March 2002

Abstract

In this paper we re-examine the American-style option pricing formula of Geske and Johnson (1984) and extend the analysis by deriving a modified formula that can overcome the possibility of non-uniform convergence encountered in the original Geske-Johnson methodology. Furthermore, we propose a numerical method, the Repeated-Richardson extrapolation, which allows us to estimate the interval of true option values and to determine the number of options needed for an approximation to achieve a given desired accuracy. Using simulation results, our modified Geske-Johnson formula is shown to be more accurate than the original Geske-Johnson formula. This paper also illustrates that the Repeated-Richardson extrapolation approach can estimate the interval of true American option values extremely well. Finally, we investigate the possibility of combining the Binomial Black-Scholes method proposed by Broadie and Detemple (1996) with the Repeated-Richardson extrapolation technique.

Keywords: American option, non-uniform convergence, Richardson extrapolation, Repeated-Richardson extrapolation

JEL Classification: G13

Suggested Citation

Chung, San-Lin and Chang, Chuang-Chang and Stapleton, Richard C., Richardson Extrapolation Techniques for the Pricing of American-Style Options (March 2002). EFMA 2002 London Meetings. Available at SSRN: https://ssrn.com/abstract=313962 or http://dx.doi.org/10.2139/ssrn.313962

San-Lin Chung (Contact Author)

National Central University at Taiwan - Department of Finance ( email )

No. 300, Jhongda Rd, Jhogli City, Taoyuan, Taiwan,
Jhongli, TY 32001
Taiwan
+886 3 422 7151 ext. 6263 (Phone)
+886 3 425 2961 (Fax)

Chuang-Chang Chang

National Central University at Taiwan - Department of Finance ( email )

No. 300, Jhongda Rd, Jhogli City, Taoyuan, Taiwan,
Jhongli, TY 32001
Taiwan
886-3-4227151 ext. 6159 (Phone)
886-3-4252961 (Fax)

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance ( email )

Curran Building
100 Cathedral Street
Glasgow G4 0LN
United Kingdom
+44 1524 381 172 (Phone)
+44 1524 846874 (Fax)

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