The Pricing Of Geometric Average Asian Option Under The Vasicek Rate Model

Asian option is one of the most active exotic options in financial derivatives trade market today, Its payoff at maturity depends not only on the price of the underlying assets that day, but also on the average of the underlying asset price in the entire period. As a kind of path-dependent option, Asian option can avoid the behavior of artificial manipulation of the underlying asset price. Because Asian option is less risky and cheaper than the standard European-style option,so it is the favorite for the investors.As the strong path dependence of Asian option, the pricing is generally more complicated. Literature[2] has studied the European geometric average Asian option pricing problem when the interest rate is constant, then we obtained the explicit expression of the pricing formula. But the interest rate,Even short-term interest rates generally are constantly changing. Therefore, assuming constant interest rates in the period is not realistic.On this basis, this paper discusses the Vasicek interest rate model which is the most common short-term interest rate model.Under this model I studied the pricing of European geometric average Asian option with a floating strike price. Firstly, we adopt the method of no-arbitrage to price the European geometric average Asian call option with floating strike price.Then we use variable substitution to reduce the dimension of the equation to two dimensions,so we get a two-dimensional Cauchy problem.Finally we solve the Cauchy equation by Fourier transformation,thus we get the pricing formula of the geometric average of Asian call option under floating interest rate.We can get the pricing formula of the geometric average of Asian put option the same way.