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STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

Published online by Cambridge University Press:  12 February 2020

Pengzhan Chen Open the ORCID record for Pengzhan Chen [Opens in a new window]  and
Wuyi Ye
Pengzhan Chen
Affiliation:
School of Management, University of Science and Technology of China, Hefei 230026, PR China E-mail: cpz@mail.ustc.edu.cn; wyye@ustc.edu.cn
Wuyi Ye
Affiliation:
School of Management, University of Science and Technology of China, Hefei 230026, PR China E-mail: cpz@mail.ustc.edu.cn; wyye@ustc.edu.cn
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Abstract

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

Keywords

jump riskmodel specificationstochastic volatilityVIX
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 513 - 531
Copyright
© Cambridge University Press 2020

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