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

doi:10.1007/s11432-017-9215-8

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	Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm
	Wang, Ximei 1,2; He, Xingkang 1,2; Bao, Ying 3; Zhao, Yanlong1,2
	2018-04-01
发表期刊	SCIENCE CHINA-INFORMATION SCIENCES
ISSN	1674-733X
卷号	61 期号:4 页码:17
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 Ito 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
DOI	10.1007/s11432-017-9215-8
语种	英语
资助项目	National Key Research and Development Program of China[2016YFB0901902] ; National Natural Science Foundation of China[61622309] ; National Basic Research Program of China (973 Program)[2014CB845301]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000428507300001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30130
专题	系统科学研究所
通讯作者	Zhao, Yanlong
作者单位	1.Chinese Acad Sci, Key Lab Syst & Control, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Ind & Commercial Bank China, Risk Management Dept, Beijing 100033, Peoples R China
推荐引用方式 GB/T 7714	Wang, Ximei,He, Xingkang,Bao, Ying,et al. Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm[J]. SCIENCE CHINA-INFORMATION SCIENCES,2018,61(4):17.
APA	Wang, Ximei,He, Xingkang,Bao, Ying,&Zhao, Yanlong.(2018).Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm.SCIENCE CHINA-INFORMATION SCIENCES,61(4),17.
MLA	Wang, Ximei,et al."Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm".SCIENCE CHINA-INFORMATION SCIENCES 61.4(2018):17.