The 256th Wenlan Financial Forum

Abstract:
Empirical evidence has shown that in terms of market uncertainty, both maxima and minima of cross-sectional stock/asset returns are driving forces. Due to the asymptotic independent property of maxima and minima of a sequence of independent random variables, existing stochastic models often only focus on one of them. This paper proposes a new dynamic stochastic model, dual-maxima-minima autoregressive conditional Frechet (DMMAcF) model, to jointly fit cross-sectional maxima and minima, and then to quantify market uncertainty through a time-varying tail risk measure and a pair of dual implied volatilities. The scale parameters (analog to volatilities) and the shape parameters (analog to volatilities of volatilities) in Frechet distributions vary conditionally on the past information. The DMMAcF model possesses unique properties such as better and faster risk estimation. Numerical experiments confirm these desired market properties. It is found that the early market crash warning effect of the DMMAcF model reacts better than existing models. (Joint work with Yu Chen and Tiantian Mao).

Speaker Introduction:
Zhengjun Zhang, professor at the School of Computer, Data & Information Sciences, University of Wisconsin; Fellow and Executive Committee Member of the Institute of Mathematical Statistics; Fellow of the American Statistical Society; Deputy Editor-in-Chief of the Journal of Business & Economic Statistics; Co-Editor of the Journal of Econometrics Special Issue on Financial Engineering and Risk Management. His research covers a wide range of topics, including fundamental dependence theory, extreme value theory and risk analysis, high-dimensional statistical learning using max-linear regression, zero-inflated protective barrier regression, variable selection based on tail limits, variable screening based on tail dependence and sure explained variability and nonlinear causal inference.