Financial Math Seminars 2013-14
The seminar in Financial Mathematics is an integral part of the program and an opportunity to interact with leading academic and industry speakers.
Seminars for the Spring Quarter are presented jointly with Operations Research (CFRA) and will be held on Wednesdays at 3:15pm in Room 370 of Building 01-370, just south of Sloan Mathematics (Math Corner) in the Main Quad.
The word analytics has nearly become cliché, with almost every major company claiming to use and create valuable analytics. StarMine, now part of Thomson Reuters, has been developing quantitative models and analytics for investment managers and other financial professionals for over 12 years. Their first success, the StarMine SmartEstimate, can predict earnings surprises with a success rate of 70%. This talk will explain some of the nuances and techniques the speaker's group employs in their quantitative modeling, and describe some of their latest research and findings.
Modeling and Estimation of Dependent Credit Rating Transitions
Simultaneous defaults in large portfolios of credit-linked securities can induce huge losses. To manage the credit risk, we introduce a framework for modeling dependent credit rating transitions, which is based on marked point processes. Under additional assumptions, the model becomes Markovian, but still allows for simultaneous credit rating transitions of the firms. We present several set-ups for this case, on of them is a homogeneous Markov jump process with the generator of the strongly coupled random walk process introduced by Spitzer (1981). The model depends on two sets of parameters, a vector of dependence parameters and the generator of the rating transitions of a single firm. For these parameters the maximum likelihood estimators can be computed using historical rating transitions and sojourn times. Simulation of the process shows, how the shape of the profit-and-loss distribution of a large portfolio of defaultable zero-coupon bonds is influenced by the dependence vector. (Based on joint work with Verena Goldammer.)
The Design of Libor and Other Interest Rate Benchmarks
Libor is a global system of interest rate benchmarks that are referenced in financial contracts whose total notional amount exceeds 300 trillion dollars. (Yes, that is trillion, not billion.) Because Libor has been mis-reported in various attempts to manipulate financial markets, new interest rate benchmarks, and new methods for estimating benchmarks based on market transactions, are being developed. This talk will discuss the benchmark design problem, drawing on work in progress for the Financial Stability Board. The modeling issues involve both economic theory and statistics.
Illiquidity and Insolvency Cascades in the Interbank Network
The great crisis of 2007-08, followed by the ongoing Euro crisis, have highlighted the need for better mathematical and economic understanding of financial systemic risk. Are there "toy models" of systemic risk that are amenable to an exact probabilistic analysis? How do these models work, how useful are they, and what are some of the conclusions that can be drawn from them? As an illustration of some of the complex issues that can be addressed, I will show how to obtain results on large graph asymptotics for systemic risk in a model in which two kinds of contagion, insolvency and illiquidity, act in opposite directions in the network.
Linear-Rational Term Structure Models
We introduce the class of linear-rational term structure models, where the state price density is modeled such that bond prices become linear-rational functions of the current state. This class is highly tractable with several distinct advantages: i) ensures non-negative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk premia, and iii) admits analytical solutions to swaptions. For comparison, affine term structure models can match either i) or ii), but not both simultaneously, and never iii). A parsimonious specification of the model with three term structure factors and at least two unspanned factors has a very good fit to both interest rate swaps and swaptions since 1997. In particular, the model captures well the dynamics of the term structure and volatility during the recent period of near-zero interest rates.