Bayesian Point Process Modeling for Extreme Value Analysis, with an Application to Systemic Risk Assessment in Correlated Financial Markets

• Activity Number: 583
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Athanasios Kottas*+ and Abel Rodriguez and Ziwei Wang
• Companies: University of California, Santa Cruz and University of California, Santa Cruz and Ask.com
• Keywords: Bayesian nonparametrics ; Dirichlet process mixture modeling ; Multivariate extreme values ; Non-homogeneous Poisson process

Abstract

We present a nonparametric Bayesian modeling framework for extreme value analysis, using the point process approach based on threshold exceedances. In particular, we focus on a modeling approach to assess the effect of systemic risks on multiple financial markets. The intensity function of extremes on each market is modeled as a superposition of two Poisson processes that can be interpreted as the systemic and idiosyncratic market risk components. In order to capture changes in the risk structure over time, the intensity function associated with each of the underlying Poisson processes is modeled using a Dirichlet process mixture of Beta densities that allows for clustering of extremes. The methodology is applied to data on extreme negative log returns of S&P500 sector indexes recorded between January 1, 2000 and December 31, 2011.