远期生效亚式期权定价的蒙特卡罗模拟法

A Monte Carlo Simulation Method for Pricing the Forward-Starting Asian Option with Floating Strike Price

由于亚式期权是以合约签定日至到期日这段时期的标的资产平均价为合约执行价,容易增加投资者的风险和成本.为了减低投资风险,研究了一类以合约生效日后某一时点起至到期日之间标的资产平均价作为执行价的远期生效亚式(FFSA)期权的定价.应用随机分析理论方法推导出几何平均的FFSA看涨期权价格的显示解,以此期权价格作为控制变量建立了算术平均的FFSA看涨期权定价的蒙特卡罗模拟算法.通过具体计算实例,分析了模型参数以及时间窗宽等因素对期权价格的影响.结果表明:带控制变量的模拟法在解决亚式期权定价,以及提高计算精度方面有重要作用.

Due to the feature of the strike price based on average asset values during some period within the option＇s lifetime, Asian options may be easy to increase risk investment. In order to reduce the risk investment, pricing forward-starting Asian options with floating-strike price （FFSA）, which is based on the underlying asset＇s average values calculated from some pre- specified time after the first trading date of the contract to maturity, was considered in this paper. Based on stochastic analysis, a closed-form solution for the FFSA call option on geometric average was firstly obtained, and the Monte Carlo simulation algorithm for the FFSA call option on arithmetic average was provided by using the variance reduction technique with the help of the above closed-form solution. We also discuss the effects of both the parameters in our model and the time windows on these options with numerical examples. The results show that the Monte Carlo simulation method with variance reduction technique plays an important role in the field of both pricing the Asian options and improving the accuracy of computation.