The recent crisis has shown the importance of the illiquidity component of credit risk.
We model, in a multi-period setting, the funding liquidity of a borrower that finances its operations through short-term debt. The short-term debt is provided by a continuum of agents with heterogeneous beliefs about the prospects of the borrower. In each period, the creditors observe the borrower’s fundamentals and decide on the amount they invest in its short-term debt. We formalize this problem as a coordination game and show that it features multiple Nash equilibria. This leads to anambiguity about the value of the barrier for the liquid net worth which would trigger the default of the borrower. Removing weakly dominated strategies allows us to eliminate the multiplicity of equilibria and determine the default barrier. The unique equilibrium is shown to be of a threshold type, a property assumed in the previous literature.
We then extend the model and show the existence of the equilibria in which the company holds cash reserves in order to increase its debt capacity, thereby offering a theoretical explanation of the cash holding puzzle.
Trading costs play a key role in active portfolio management, the hedging of derivative securities, and other optimal investment problems. However, the corresponding optimization problems typically are rather intractable, even in simple concrete models. In this talk, we discuss explicit solutions that can be obtained in the limit for small costs. These show how to implement frictionless trading strategies in an optimal manner, and thereby reveal some of the salient features of portfolio choice with frictions.
The Hopkins Undergraduate Society for Applied Mathematics is excited to present Dr. Joseph McCloskey, Senior Cryptographic Mathematician at the National Security Agency. Dr. McCloskey will be discussing his background and work with the NSA, as well as similar opportunities for applied mathematicians, statisticians, and computer scientists.
Self-exciting point processes are simple point processes that have been widely used in neuroscience, sociology, finance and many other fields. In many contexts, self-exciting point processes can model the complex systems in the real world better than the standard Poisson processes. We will discuss the Hawkes process, the most studied self-exciting point process in the literature. We will talk about the limit theorems and asymptotics in different regimes. Extensions to Hawkes processes and applications to finance will also be discussed.
We introduce a framework for computing the total valuation adjustment (XVA) of an European claim accounting for funding costs, counterparty risk, and collateral mitigation. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs) associated with the replicating portfolios of long and short
positions in the claim. This leads to defining buyer and seller’s XVAs which in turn identify a no-arbitrage band. When borrowing and lending rates coincide we provide a fully explicit expression for the uniquely determined price of XVA. When they differ, we derive the semi-linear partial differential equations (PDEs) associated with the non-linear BSDEs. We use them to conduct a numerical analysis showing high sensitivity of the no-arbitrage band and replicating strategies to funding spreads and collateral levels. This is joint work with Agostino Capponi (Columbia) and Stephan Sturm (WPI).
Responding to the low interest rate environment prevailing since the early 2000’s, banks introduced equity derivative options, called minimum coupon (or globally floored) cliquets, designed to have high potential payouts but at low premium cost. Cliquet prices are heavily dependent on volatility skew at forward points in time. Unforuntately, forward skew can not be directly observed from vanilla option prices. I will discuss some of common methods for estimating forward skew and highlight their advantages and disadvantages.
John Urschel is a football player for the Baltimore Ravens; this past year he played in 11 games. He is also an accomplished
mathematician, the first-author of a paper in the Journal of Computational Mathematics, in which he developed fast numerical methods of computing the eigenvector associated with the second smallest eigenvalue of a graph Laplacian. How does his professional football experience relate to the esoteric world of cutting-edge mathematical research?
Join HUSAM in welcoming John to share his fascinating intersection of the gridiron and numerical analysis at the highest levels.
Lies, Deceit, and Misrepresentation: The Distortion of Statistics in America
H.G. Wells once said “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” The widespread use of statistics plays an influential role in persuading public opinion. As such, statistical literacy is necessary for members of society to critically evaluate the bombardment of charts, polls, graphs, and data that are presented on a daily basis. However, what often passes for “statistical” calculations and discoveries need to be taken with a grain of salt. This talk will examine the applications of statistics in American media and give examples of where statistics has been grossly misused.
The talk will begin at 7pm in Hodson 110, with refreshments being served at 6:30. A flyer for the event is attached and a link to RSVP on the Facebook page is here: https://www.facebook.com/events/959982947374497/.