Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm  

作　　者：Ximei WANG Xingkang HE Ying BAO Yanlong ZHAO 

机构地区：[1]Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China [2]School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China [3]Risk Management Department, Industrial and Commercial Bank of China, Beijing 100033, China

出　　处：《Science China(Information Sciences)》2018年第4期128-144,共17页中国科学（信息科学）（英文版）

基　　金：supported by National Key Research and Development Program of China(Grant No.2016YFB0901902);National Natural Science Foundation of China(Grant No.61622309);National Basic Research Program of China(973 Program)(Grant No.2014CB845301)

摘　　要：Heston model is the most famous stochastic volatility model in finance. This paper considers the parameter estimation problem of Heston model with both known and unknown volatilities. First, parameters in equity process and volatility process of Heston model are estimated separately since there is no explicit solution for the likelihood function with all parameters. Second, the normal maximum likelihood estimation（NMLE） algorithm is proposed based on the It？o transformation of Heston model. The algorithm can reduce the estimate error compared with existing pseudo maximum likelihood estimation. Third, the NMLE algorithm and consistent extended Kalman filter（CEKF） algorithm are combined in the case of unknown volatilities. As an advantage, CEKF algorithm can apply an upper bound of the error covariance matrix to ensure the volatilities estimation errors to be well evaluated. Numerical simulations illustrate that the proposed NMLE algorithm works more efficiently than the existing pseudo MLE algorithm with known and unknown volatilities. Therefore, the upper bound of the error covariance is illustrated. Additionally, the proposed estimation method is applied to American stock market index S＆P 500, and the result shows the utility and effectiveness of the NMLE-CEKF algorithm.Heston model is the most famous stochastic volatility model in finance. This paper considers the parameter estimation problem of Heston model with both known and unknown volatilities. First, parameters in equity process and volatility process of Heston model are estimated separately since there is no explicit solution for the likelihood function with all parameters. Second, the normal maximum likelihood estimation（NMLE） algorithm is proposed based on the It？o transformation of Heston model. The algorithm can reduce the estimate error compared with existing pseudo maximum likelihood estimation. Third, the NMLE algorithm and consistent extended Kalman filter（CEKF） algorithm are combined in the case of unknown volatilities. As an advantage, CEKF algorithm can apply an upper bound of the error covariance matrix to ensure the volatilities estimation errors to be well evaluated. Numerical simulations illustrate that the proposed NMLE algorithm works more efficiently than the existing pseudo MLE algorithm with known and unknown volatilities. Therefore, the upper bound of the error covariance is illustrated. Additionally, the proposed estimation method is applied to American stock market index S＆P 500, and the result shows the utility and effectiveness of the NMLE-CEKF algorithm.

关 键 词：Heston model stochastic volatility model parameter estimation normal maximum likelihood estimation pseudo maximum likelihood estimation consistent extended Kalman filter 

分 类 号：O212[理学—概率论与数理统计]