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Parameter estimates of Heston stochastic volatility model with MLE and consistent EKF algorithm
Wang, Ximei1,2; He, Xingkang1,2; Bao, Ying3; Zhao, Yanlong1,2
2018-04-01
Source PublicationSCIENCE CHINA-INFORMATION SCIENCES
ISSN1674-733X
Volume61Issue:4Pages:17
AbstractHeston 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.
KeywordHeston model stochastic volatility model parameter estimation normal maximum likelihood estimation pseudo maximum likelihood estimation consistent extended Kalman filter
DOI10.1007/s11432-017-9215-8
Language英语
Funding ProjectNational 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 Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000428507300001
PublisherSCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30130
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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