Geometric Average Asian Option Pricing With Stochastic Interest Rate Under The Condition Of Fractional Brown Motion Environment

In recent years, as the financial market gradually improved, Seek a high return on investment and avoid the financial risk has become the urgent demand of all financial investors. Options as a special kind of financial derivatives on the basis of the traditional basic financial instruments, come into being based on the demand of investors to avoid financial risks. Asian option is a new type of special options invented by financial engineer in the derivatives market, with the adoption of the average price of the asset in effective period, the volatility of the Asian option is reduced.A large number of empirical studies found that the actual financial market of the stock price process show some fractal characteristics,Such as self-similarity, long-term memory, etc.This does not conform with the classic B-S pricing theory.In this paper, we study two types of geometric average Asian option (the fixed strike price Asian option and the floating strike price Asian option) pricing problem under the condition that the underlying asset price follows fractional Brown motion and the interest rate meet the Hull-White (single factor) model. And deduced the corresponding pricing formula and put-call parity equation.