【题目】Maximum Likelihood Estimation of Latent Markov Models Using Closed-Form Approximations




【摘要】This paper proposes and implements an efficient and flexible method to compute maximum likelihood estimators of continuous-time models when part of the state vector is latent. Stochastic volatility and term structure models are typical examples. Existing methods integrate out the latent variables using either simulations as in MCMC, or replace the latent variables by observable proxies. By contrast, our approach relies on closed-form approximations. The method makes it possible to estimate parameters of multivariate Markov models with latent factors and simultaneously infer the distribution of filters, i.e., that of the latent states conditioning on observations. Without any particular assumption on the filtered distribution, we approximate in closed form a coupled iteration system for updating the likelihood function and filters based on the transition density of the state vector. Our procedure has a linear computational cost with respect to the number of observations, as opposed to the exponential cost implied by the high dimensional integral nature of the likelihood function. We prove the convergence of our method as the frequency of observation increases and conduct Monte Carlo simulations to demonstrate its performance.

【主讲人简介】李晨煦,2018年博士毕业于北京大学光华管理学院商务统计与经济计量系,随后在普林斯顿大学本德海姆金融中心师从国际著名的金融经济学家Yacine Aït-Sahalia教授进行博士后工作。他的主要研究方向为金融计量、金融工程和随机建模等。目前,他已经完成多篇高质量工作论文,并有多篇论文分别在计量经济学和金融学的国际顶级期刊的第二轮或第三轮修改中。


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