Speaker: Professor Liu Zhi
Topic: Realized Copula of Volatility
Date: December 26th, 2025 (Friday)
Time: 4.00 p.m.-5.00 p.m.
Venue: Lecture Hall 304, Building 6, Yunlong Campus
Sponsors: School of Mathematics and Statistics, Institute of Mathematics, Institute of Science and Technology
Biography:
Liu Zhi is a professor in the Department of Mathematics at the University of Macau, with research interests including Statistics for Stochastic Processes, Financial Statistics, and Statistical Learning for Health Science. His research papers have been published in international journals in statistics and its interdisciplinary fields, such as statistics journals Annals of Statistics, Journal of American Statistical Association, Journal of Business and Economic Statistics, econometrics journals Quantitative Economics, Journal of Econometrics, Econometric Theory, Econometrics Journal, finance journals Journal of Banking and Finance, Finance and Stochastics, bioinformatics journal Bioinformatics, as well as AAAI. In addition, he has presided over more than 10 projects funded by the National Natural Science Foundation of China and Macao Government.
Abstract:
Asset empirical volatility is random. The statistical inference on the volatility itself, conditional on the volatility path, has been well established. However, the inference on the distribution of the stochastic volatility is yet to be well studied, particularly for the multivariate case. In the work, we study the copula of the distributions of bivariate stochastic volatility. We propose realized copula based on estimators of the spot volatility, and establish both infill and long-span asymptotics. Simulation studies based on two well-known stocahstic volatility models, Heston model and OU process, demonstate good performance of our realized copula in capturing the joint distributional pattern of the bivariate stochastic volatility. We also implement our realized copula to a real high-frequency data including two futures contracts, the E-mini S&P 500 (ES) and the 10-Year Treasury Notes (TY). The results suggest a Gumbel copula with a parameter around 1.6 for two stochastic volatilities. This is a joint work with Kim Christensen, Wenjing Liu and Yoann Potiron.