跳–扩散模型参数校准的极大似然法

The Maximum Likelihood Method for the Calibration of Parameter under Jump-Diffusion Models

摘要: 首先用蒙特卡洛罗法模拟生成股票的价格路径，然后对生成的路径建立对数似然函数。假设跳–扩散模型的股票市场价格与模型价格之间存在高斯误差，构造权重函数，通过线性搜索的方法求解加权极大似然函数的最大化，从而得到波动率的校准。最后给出数值模拟实验，实验结果表明了该算法的可行性。

Abstract: First, the Monte Carlo method is given to simulate the generation of the stock price path, and then the logarithmic likelihood function is established for the generated path. Assuming that there is a Gauss error between the stock market price and the model price, we construct the weight function and maximize the weighted maximum likelihood function using the linear search method, thus the calibration of volatility is obtained. At last, the numerical simulation experiments are given, the experimental results show the feasibility of the algorithm.