The Approximate Analytical Approach To Price American Option

American options pricing can be attributed to optimal stopping problems or variational i-nequalities problems, in general, there is no closed form pricing formula. Pricing for such opt-ions, we commonly used methods as follows:the method of Monte Carlo simulation[12,13] and semi-analytical approximations [4,5]. Recently, literature[22] introduced an approach to price American options which using an asymptotic expansion and tractable. Semi-analytical appro-ximations are fast and accurate, but they cannot easily be extended beyond the Black-Scholes models. The main advantage of this method lies in its straightforward extension to multifactor models with stochastic volatility and stochastic interest rates, but it only provides third-order expansion, what’s more, it cannot extension to multifactor models. Inspired by literature[22], this paper mainly do three things:Derive the general formula of pricing American options; using an explicit and intuitive rule proxy for the optimal exercise rule, we generalize our appr-oach to three-model with stochastic volatility and stochastic interest rates; using some numeri-cal experiments and results proved the convergence and accuracy of our approach. Our appro-ach is based on the idea of substituting the optimal exercise rule with a approximate optimal exercise rule.This paper is divided into four parts:Chapter1, we introduced the related concepts about option and the investigation status of American option pricing. Necessary preparations for as-ymptotic expansion approach to price American options under Black-Scholes model are prov-ided and introduces the definition of Normalized moneyness in Chapter2. In Chapter3derive the general formula of pricing American options. In Chapter4extension our approach to mul-tifactor models with stochastic volatility and stochastic interest rates,given some numerical e-xperiments and results proved the convergence and accuracy of our approach.