PRICING CONTINUOUSLY SAMPLED ASIAN OPTIONS WITH PERTURBATION METHOD JIN E. ZHANG This article explores the price of continuously sampled Asian options. For geometric Asian options, we present pricing formulas for both backward- starting and forward-starting cases. For arithmetic Asian options, we demonstrate that the governing partial differential equation (PDE) cannot be transformed into a heat equation with constant coefficients; therefore, these options do not have a closed-form solution of the Black–Scholes type, that is, the solution is not given in terms of the cumulative normal distribution function. We then solve the PDE with a perturbation method and obtain an analytical solution in a series form. Numerical results show that as compared with Zhang’s (2001) highly accurate numerical results, the series converges very quickly and gives a good approximate value that is more accurate than any other approximate method in the literature, at Earlier versions of this article have been circulated under the title “Theory of Continuously Sampled Asian Option Pricing.” The author acknowledges helpful comments and suggestions from Phelim Boyle, Nengjiu Ju, two anonymous referees, and seminar participants and discussants at the Asia Pacific Finance Association Annual (APFA 2001) Conference, Hong Kong University of Science and Technology, University of Wollongong, and University of Technology in Sydney. The author thanks Tiecheng Li, Benlong Wang, Yi Xiang, Ming Yuan, and Shuguang Zhang for their discussions and assistance. This article has been supported by the Research Grants Council of Hong Kong under grant CERG-1068/01H. For correspondence, J. E. Zhang, Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; e-mail: jinzhang@ust.hk Received June 2002; Accepted November 2002 ■ Jin E. Zhang is affiliated with the Department of Finance at Hong Kong University ofScience and Technology in Clear Water Bay, Kowloon, Hong Kong. The Journal of Futures Markets, Vol. 23, No. 6, 535–560 (2003) © 2003 Wiley Periodicals, Inc. Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fut.10073