  In this paper, a standard PDE for the pricing of arithmetic average strike
Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher
Order Compact finite difference scheme for this pricing problem is derived.
Both these schemes were implemented for various values of risk free rate and
volatility. The option prices for the same set of values of risk free rate and
volatility was also computed using Monte Carlo simulation. The comparative
results of the two numerical PDE methods shows close match with the Monte Carlo
results, with the Higher Order Compact scheme exhibiting a better match. To the
best of our knowledge, this is the first work to use the numerical PDE approach
for pricing Asian call options with average strike.
