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Approximation of eigenvalues of spot cross volatility matrix with a view toward principal component analysis

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Abstract

In this paper we introduce some estimators for the eigenvalues of the spot cross volatility matrix of a multidimensional diffusion process. We establish limit theorems for the new estimators and study their numerical performance on a stochastic volatility model of Heston type.

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Acknowledgements

The authors would like to thank Jiro Akahori, Freddy Delbaen, Arturo Kohatsu-Higa, Maria Elvira Mancino, and Shigeyoshi Ogawa for their helpful comments. The first author was supported by JSPS Grant-in-Aid for Young Scientists (B) number 25780213. This work was completed while the second author was staying at Vietnam Institute for Advanced Study in Mathematics (VIASM) and he would like to thank the institute for support. The authors are also grateful to the referee for her/his valuable comments which led to the improvement of the paper.

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Authors and Affiliations

  1. Research Organization of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, Japan

    Nien-Lin Liu & Hoang-Long Ngo

  2. Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Hoang-Long Ngo

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  1. Nien-Lin Liu
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  2. Hoang-Long Ngo
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Correspondence to Nien-Lin Liu.

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Liu, NL., Ngo, HL. Approximation of eigenvalues of spot cross volatility matrix with a view toward principal component analysis. Japan J. Indust. Appl. Math. 34, 747–761 (2017). https://doi.org/10.1007/s13160-017-0266-8

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  • DOI: https://doi.org/10.1007/s13160-017-0266-8

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