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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。
The least square Monte Carlo (LSM) method is used to study the American option pricing under stochastic interest rate. Firstly, the market model of the underlying stock price and short-term interest rate is established and transformed into the risk-neutral probability space. Then, the calculation steps of the LSM method of the American option under the random interest rate are obtained. On this basis, the numerical simulation under certain parameters is carried out, and the effect of stochastic interest rate on the pricing of American options is obtained, and the validity of the method is verified.