Analytic approximation formulae for pricing forward-starting Asian options

In this article we first identify a missing term in the Bouaziz, Briys, and Crouhy (1994) pricing formula for forward-starting Asian options and derive the correct one. First, illustrate in certain cases that the missing term in their pricing formula could induce large pricing errors or unreasonable option prices, Second, we derive new analytic approximation formulae for valuing forward-starting Asian options by adding the second-order term in the Taylor series. We show that our formulae can accurately value forward-starting Asian options with a large underlying asset's volatility or a longer time window for the average of the underlying asset prices, whereas the pricing errors for these options with the previously mentioned formula could be large. Third, we derive the hedge ratios for these options and compare their properties with those of plain vanilla options.