Research On Problems Of Asian Option Pricing

In this paper we considered three problems on Asian options pricing: The valuation of geometric average Asian options with stochastic averaging period, the valuation of Asian options with fixed strike price and floating strike price in the case of arithmetic average.Firstly, we set a barrier to the underlying asset price under the assumption of common Asian options, the average period begins at the first time when the underlying price hits the barrier. We give a closed-form formula for the Asian call options price with fixed strike price in the case of continuous geometric average and in the case of discrete geometric average.Secondly, under the consumption that the process of underlying asset price is a geometric Brownian motion, in other words, the probability distribution function of it is lognormal, we approximate the average of underlying price using a lognormal stochastic variable with the same first two-order moment. We give the approximation formula for Asian call options price with fixed strike price in the case of continuous arithmetic average and in the case of discrete arithmetic average.In the end, we study the Asian options with floating strike price in the case of arithmetic average. We improved the results of Bouaziz et al by a two-order Taylor expansion, and give a more accurate approximation formula to the price of call option.