Accurate pricing formulas for Asian options

Asian options have payoffs that depend on the average price of the underlying asset such as stocks, commodities, or financial indices. As exact closed-form formulas do not exist for these popular options, how to price them numerically in an efficient and accurate manner has been extensively investigated. There are two types of Asian options, fixed-strike and floating-strike Asian options. Excellent lower-bound formulas for both types of options have been derived by Rogers and Shi. These formulas are extremely easy to calculate, but they restrict the option's maturity to exactly 1 year. This paper extends the Rogers-Shi formulas to general maturities. Numerical experiments are performed to compare the formulas with many other numerical methods in the literature and under a wide variety of situations. They confirm the extreme accuracy of the formulas.