随机利率下美式期权的LSM方法定价

Pricing American Option by LSM Method under Stochastic Interest Rate

运用最小二乘蒙特卡罗(LSM)方法对随机利率下的美式期权定价进行研究。首先建立了标的股票价格与短期利率的市场模型,并将其转换到风险中性概率空间中,然后得到了随机利率下美式期权的LSM方法的计算步骤。在此基础上,进行了确定参数下的数值模拟,得到了随机利率对美式期权定价的影响,并验证了该方法的有效性。

This paper uses the least-squares Monte Carlo （LSM） method to price the American option under the stochastic interest rate. Firstly, the stock price process and the short interest rate process are modelled, and they are converted to the models in the risk neutral probability space. Then, the calculation steps of LSM method to American option pricing under the stochastic interest rate are obtained. Furthermore, the numerical simulation is made with the determinate parameters which demonstrate the effect of the stochastic interest rate on American option pricing and the validity of the LSM method.