A P.D.E. Approach to Asian Options: Analytical and Numerical Evidence

We first derive a one state variable partial differential equation, easy to emplement, which characterizes the price of a European type Asian option. This result is explained and related to previous literature. When we derive new results on the hedging of an Asian option and propose analytical and numerical analysis on the comparison between Asian and European options. Our methodology which applies to fixed-strike Asian options as well to floating-strike Asian options completes and clarifies various results in the literature. In this paper we focus on backward-starting Asian options. Our approach is quite general however, and we explain how to adapt our main results to the case of forward-starting Asian options.