STATISTICS COLLOQUIUM
László Márkus
Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary,
and
Department of Statistics, University of Connecticut
Rough Stochastic Correlation for Modeling Tail Dependence of Asset Price Pairs
Abstract
In 2009 the magazine Wired published. ”Recipe for Disaster: The Formula That Killed Wall Street” as the cover story written by journalist Felix Salmon. It blames the subprime crisis on the Gaussian copula, which was then used in finance as industry standard to estimate the probability distribution of losses on a pool of loans or bonds or assets. The Gaussian copula cannot, indeed, create tail dependence, crucial in modeling simultaneous defaults, but that was known before the crisis, as were other models, capable to do so. More than 10 years passed by since then, but the various copula and other models in use, going beyond correlation for describing dependence, do not harmonize well with the stochastic differential equation (SDE) description used for individual assets. Those models are often evaluated on the basis of their performance in option pricing, putting them to the test by relatively few data and short time period. In the lecture I build up an approach where interdependence is inherent from the covariations of Brownian motions driving the asset equations. These covariations in turn are integrals of suitable SDE driven stochastic processes called stochastic correlations. We test the goodness of the suggested model on historic asset price data, by using Kendall functions of copulas. The paradigm of rough paths leads to a newly emerging methodology in modeling stochastic volatility of assets. We suggest a similar approach to the mentioned stochastic correlations, and show that in frequent, minute-wise trade the fractal dimensions support the assumption of rough paths. The developed model helps showing that similar herding behavior of brokers as expressed by the HIX index may lead to very different tail dependence and hence e.g. variable probabilities of coincident defaults. The model may also be useful e.g. in CDO pricing, and in Credit Value Adjustment (CVA). A positive correlation/association between exposure and counterparty default risk gives rise to the so called Wrong-Way Risk (WWR) in CVA. Even though roughly two-thirds of the losses in the credit crisis were due to CVA losses, a decade after the crisis addressing WWR in a both sound and tractable way remains challenging. Our suggested model is capable of creating tail dependence, and produces more realistic CVA premiums than constant correlations.
DATE: Friday, January 17, 2020
TIME: 11:00 am
PLACE: Philip E. Austin Bldg., Rm. 344
Coffee will be served at 10:30 am in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu