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A Quasi‐Analytical Pricing Model for Arithmetic Asian Options
Author(s) -
Sun Jianqiang,
Chen Langnan,
Li Shiyin
Publication year - 2013
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.21576
Subject(s) - mathematics , asian option , geometric mean , log normal distribution , approximation error , volatility (finance) , black–scholes model , valuation of options , statistics , arithmetic , econometrics
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