Join us for the Brooklyn Quant Experience (BQE) Lecture Series on Thursday, February 24th at 6 pm ET on Zoom.

“Dependent Stopping Times and an Application to Credit Risk Theory”

Alejandra Quintos Lima
Ph.D. Candidate in Statistics
Columbia University

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*Please note a meeting password is required for this event.
Meeting ID: 983 0682 8534
Password: BQEAQL224

Abstract

Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.

In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy’s state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.

Bio
Alejandra is finishing her Ph.D. in Statistics at Columbia University under the direction of Prof. Philip Protter. Her research interests lie primarily in problems in probability, stochastic processes, and statistics motivated by their applications, particularly those applications in mathematical finance. During her Ph.D. program, Alejandra held a Fulbright grant, and she was one of the finalists for the 2021 Presidential Awards for Outstanding Teaching by a Graduate Student at Columbia University. Before graduate school, she worked for Citigroup in Mexico, participated in a summer research program at Cornell University, and did an internship in DC. She held a merit scholarship to major in Actuarial Sciences in UDLAP (Puebla, Mexico) where she graduated as Summa Cum Laude and was the Valedictorian of her class.

Join us for the Brooklyn Quant Experience (BQE) Lecture Series on Thursday, February 17th at 6 pm ET on Zoom.

“James-Stein Estimation of Minimum Variance Portfolios”

Alex Shkolnik
Assistant Professor
University of California Santa Barbara

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*Please note a meeting password is required for this event.
Meeting ID: 984 1537 6549
Password: BQEAS217

Abstract
In quantitative finance, estimated covariance matrices are routinely used to construct portfolios with mean-variance optimization. It is widely recognized, however, that the embedded sampling error tricks the optimizer into constructing distorted and highly inefficient portfolios. This problem is further amplified when the number of securities vastly exceeds the number of observations. We quantify this inefficiency with a metric we call the optimization bias which depends primarily on the leading eigenvector of a sample covariance matrix. Under a spiked covariance model, we prove that the optimization bias may be completely erased given just two observations of the security return but provided that the number of securities tends to infinity. We illustrate the theory with numerical simulations that provide further insight into the behavior of the proposed estimator in practice. We conclude the talk by establishing rich connections between the Stein paradox in statistics, the beta adjustments commonly used in the financial industry, and the James-Stein estimator of a principal component.

Bio
Alex Shkolnik is an Assistant Professor at the Department of Statistics and Applied Probability at the University of California, Santa Barbara, and a Research Fellow at the Consortium for Data Analytics in Risk at the University of California, Berkeley where he was a postdoctoral scholar. Alex received his Ph.D. in computational mathematics and engineering from Stanford University in 2015. His research interests include Monte Carlo simulation, high-dimensional statistics, and quantitative financial risk management.

The Brooklyn Quant Experience (BQE) Lecture Series returns for the Spring 2022 semester on Thursday, February 10th at 6 pm ET on Zoom.

A Gentle Introduction to Adjoint Algorithmic Differentiation (AAD):
(How to Better Hedge Financial Risk, Crack Some Puzzles of Condensed Matters and Much More with Upside-Down Derivatives)

Luca Capriotti
Global Head of Quantitative Strategies
Credit Suisse

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*Please note a meeting password is required for this event.
Meeting ID: 998 1185 8126
Password: BQELC210