Efficient solutions for discrete Asian options

While in the literature most studies on pricing focus on continuous Asian options, in this paper we provide efficient solutions for both European and American discrete average price Asian options. The method used for deriving the approximation formula for European Asian options is based on the idea of Bouaziz et al. (J Bank Finance 18:823-839, 1994) and Taso et al. (J Futures Mark 23:487-516, 2003) in which the Taylor expansion is used to obtain the approximation formula for continuous average strike Asian options. By using the Taylor expansion to the second order, a simple and accurate solution can be obtained. The approximation formula for the European Asian option can further be used to enhance the efficiency of the pricing of the American Asian options when using the numerical method.