All colloquia will be held at 4PM in AUST 344, unless otherwise noted. Coffee will be served at 3:30PM in AUST 326.
Information about past colloquia is available here.
|Friday, January 17||László Márkus, University of Connecticut||Rough Stochastic Correlation for Modeling Tail Dependence of Asset Price Pairs||11AM in AUST 344. Coffee at 10:30PM in AUST 326.|
|Wednesday, January 22||Emmy Karim, University of Connecticut||Construction of Simultaneous Confidence Intervals for Ratios of Means of Lognormal Distributions||4PM in AUST 344. Coffee at 3:30PM in AUST 326.|
|Wednesday, January 29|
|Wednesday, Feburary 5|
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
January 17, at 11AM in AUST 344
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.
Emmy Karim; Assistant Professor-in-Residence, Department of Statistics, University of Connecticut
Construction of Simultaneous Confidence Intervals for Ratios of Means of Lognormal Distributions
January 22, at 4PM in AUST 344
For constructing simultaneous confidence intervals for ratios of means for lognormal distributions, two approaches using a two-step method of variance estimates recovery are proposed. The first approach proposes fiducial generalized confidence intervals (FGCIs) in the first step followed by the method of variance estimates recovery (MOVER) in the second step (FGCIs–MOVER). The second approach uses MOVER in the first and second steps (MOVER–MOVER). Performance of proposed approaches is compared with simultaneous fiducial generalized confidence intervals (SFGCIs). Monte Carlo simulation is used to evaluate the performance of these approaches in terms of coverage probability, average interval width, and time consumption.