Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach
针对连续时间扩散过程仅离散观测时似然函数不可显式计算的问题，本文用Hermite多项式构造闭式函数序列逼近真实似然函数，证明其收敛性及估计量的渐近性质，蒙特卡洛证据表明该方法在金融模型中优于其他逼近方案。
When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.