运用Matlab基于LSM方法对美式期权定价的新探究

New Explorations about American Option Pricing by Applying Matlab Based on LSM

传统期权定价方法是通过主观假定初始价格、执行价格、期限、波动率、无风险利率等条件来对期权进行定价,很少联系实际的期权市场报价对期权进行定价。本文根据股票期权市场报价,通过Matlab快速方便地求解出隐含的波动率和无风险利率,并在此基础上运用Matlab基于最小二乘蒙特卡洛模拟(LSM)方法对该股票的美式期权进行定价。本文揭示了如何根据期权市场报价实现隐含波动率和无风险利率的求解,进而结合LSM方法对美式期权进行定价的一种新方法。此外,本文对LSM方法的改进技术也进行了探讨。

The traditional option pricing method usually prices the option through conditions such as the initial price, executive price, term, volatility ratio and risk-free interest rate, which seldom prices the option by connecting with the quoted option market price. Based on the quoted option market price, this paper calculates the implied volatili- ty and risk-free interest rate fast and conveniently through Matlab. And by applying Matlab based on LSM, we can price American option. This article shows how to calculate the implied volatility and risk-free interest rate according to the quoted option market price, and the method to price American option which combines LSM. In addition, this pa- per also probes into the improved technology of LSM.