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

【主講人】李晨煦博士，普林斯頓大學(xué)本德海姆金融中心博士后

【時(shí)間】2019年12月19日下午14:00-15:00

【地點(diǎn)】中國人民大學(xué)明德主樓623

【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.

【主講人簡介】李晨煦，2018年博士畢業(yè)于北京大學(xué)光華管理學(xué)院商務(wù)統(tǒng)計(jì)與經(jīng)濟(jì)計(jì)量系，隨后在普林斯頓大學(xué)本德海姆金融中心師從國際著名的金融經(jīng)濟(jì)學(xué)家Yacine A?t-Sahalia教授進(jìn)行博士后工作。他的主要研究方向?yàn)榻鹑谟?jì)量、金融工程和隨機(jī)建模等。目前，他已經(jīng)完成多篇高質(zhì)量工作論文，并有多篇論文分別在計(jì)量經(jīng)濟(jì)學(xué)和金融學(xué)的國際頂級期刊的第二輪或第三輪修改中。

編輯:楊菲；核稿:章永輝