A Quasi-Analytical Pricing Model for Arithmetic Asian Options

Authors

  • Jianqiang Sun,

    Corresponding author
    • Jianqiang Sun is an Associate Professor of Finance at the School of Economics and Commerce, South China University of Technology, Guangzhou, People's Republic of China
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  • Langnan Chen,

    1. Langnan Chen is a Professor of Finance and Economics at the Lingnan (University) College and Institute for Economics, Sun Yat-sen University, Guangzhou, People's Republic of China
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  • Shiyin Li

    1. Shiyin Li is an Associate Professor of Mathematics at the School of Mathematical Science, Xiamen University, Xiamen, People's Republic of China
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  • We thank Bob Webb (the editor) and an anonymous referee for their helpful comments and suggestions. The study is supported by China Social Science Foundation under grant nos. 09CJY013 and 08AJL007, China Natural Science Foundation under grant no. 70673116 and 2012 urgent Project, Humanities and Social Sciences Foundation of Chinese Ministry of Education under grant no. 08JC790038, Guangdong Philosophy and Social Science Foundation under grant nos. 08YE-02 and GD10CYJ01, Guangdong Social Science Project under grant no. 08JDXM79001, the 985 Project, and the Fundamental Research Funds for the Central Universities under nos. x2jmD2117980 and x2jmD2117990.

Correspondence author, School of Economics and Commerce, South China University of Technology, Guangzhou, Guangdong 510006, People's Republic of China. Tel: +86–20-39380756, Fax: +86–20-39381068, e-mail: jqsun@scut.edu.cn

Abstract

We develop a quasi-analytical pricing method for discretely sampled arithmetic Asian options. We derive an asymptotic approximation of the arithmetic average with the geometric average of lognormal variables. Numerical experiments show that the asymptotic approximation is accurate and the absolute error converges very quickly as the number of observations increases. The absolute error is of the order of 10−5 to 10−6 for daily average. We then derive quasi-analytical formulas for arithmetic Asian options under the Black–Scholes framework, in which the probability density of the geometric average is used. Extensive experiments are conducted to compare the proposed method with the various existing semianalytical methods. The overall accuracy of the proposed method is better than any other methods tested. The proposed method performs much better than the second best one for at-the-money Asian options under high volatility. The mean pricing error of the proposed method for a daily average Asian option is 37.5% less than the second best one. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:1143–1166, 2013

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