Finite Difference Schemes for Black-Scholes with Asian Option

Asian option is quite different from European option which can be exercised on the date of expiration, and not like the American option which exercised anytime during the period of contract. It is an unusual derivative that the option payoff depends on the average of a stock price or underlying asset over a certain period in the future. There are some demands from real world application. The attractive point is that Asian option is cheaper than the other options to hedge the similar risk. In addition, some investors need security which can protect them from the volatility and risk from the market, at the same time, the average option can provide an investor with a greater level of flexibility to make a deal. This paper focus on the point that using Finite-difference method to solve the Black-Scholes partial differential equation for the Asian Option valuation problem.