The Pricing Of Geometric Average Asian Option And The Parameter Sensitivity Analysis

Option is one of derivative financial instruments, the core problem about options is the option pricing. In recent years, in order to adapt the actual situation of financial markets and satisfy the needs of more investors, financial institutions have designed dif-ferent types of exotic options. Asian option is one of new options whose terminal payoff depends on average price of the underlying asset over a part or the whole of the option’s life. Many scholars have studied the Asian option’s valuation. In this paper we will continue to discuss the Asian option pricing.Firstly, we give some assumptions about the market, Ito’s formula and the properties of Ito’s integral, including the properties of gaussian distribution, isometric formula, etc.Secondly, we suppose the underlying asset price S(t) follows geometric Brownian motion and pays dividends yield q(t), and risk-free rate r(t) follows Vasicek extension model. By using Ito’s formula and some analysis techniques, we obtain the expression of r(t) and S(t). The pricing formulas of the fixed strike Asian option with geometric averaging are given. In the results, we use zero coupon bond prices P(t,T) to replace the risk-free interest rate r(t), extending the original results. In addition, by the help of change of measure and martingale method we get the pricing of the floating strike Asian options with geometric average under stochastic interest rate. For the pricing of the floating strike Asian options with geometric average, scholars have given the resules by soluting the partial differential equations. Their proofs are cumbersome and complicated. Our approach simplifies the proof and improves their results.Thirdly, taking into account asset prices may be affected by certain major events and show occasional jumps, we assume the underlying asset follows jump diffusion model. Using the risk neutral pricing approach we get the pricing formulas of the fixed strike Asian option with geometric averaging.Finally, based on the pricing formula, we analyze the sensitivity of the geometric average Asian option price with respect to parameter:S, γ, σ, T, which allows us a deeper understand to Asian option.