Credit Risk Workshop

19 T.W. Alexander Drive
P.O.Box 14006
Research Triangle Park, NC 27709-4006
Tel: 919.685.9350
Fax: 919.685.9360
info@samsi.info

Peter Bloomfield
North Carolina State University
Department of Statistics
bloomfield@stat.ncsu.edu

Title and Abstract TBA

Rene Carmona
Princeton University
Department of Operations Research & Financial Engineering
rcarmona@princeton.edu

“Endogenous Time of Default”

We review several forms of the classical Leland's model of the capital structure of a leveraged firm and we give numerical evidence of the changes in the optimal time of default when options are added to the initial mix equity/debt.

Nan Chen
Columbia University
Department of Industrial Engineering and Operations Research
nc2005@columbia.edu

“Credit Spreads, Capital Structure, and Implied Volatility with Endogenous Default and Jump Risk”

We propose a two-sided jump model for credit risk by extending the Leland-Toft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenuous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) The jump and endogenuous default can produce a variety of non-zero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The two-sided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; and although in general credit spreads and implied volatility tend to move in the same direction under exogenous default models, but this may not be true in presence of endogenuous default and jumps. In terms of mathematical contribution, we give a proof of a version of the “smooth fitting” principle for the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model.

Pierre Collin-Dufresne
Goldman Sachs
Department of Quantitative Strategies
pierre.collin-dufresne@gs.com

“Credit Spreads and Credit Risk Premia”

Peter Cotton
Morgan Stanley
Department of Fixed Income
peter.cotton@morganstanley.com

“There are Hard Problems in Finance”

Most sensible scientific approaches to the management and trading of portfolio credit products, hybrids and complex products run up against reasonably tough mathematical or computational hurdles. Furthermore, it is not difficult to speculate on the future directions for sell side financial engineering when such problems will be all the more important. I will argue that attempts to circumvent these are naive, that progress can be made, and that meaningful cooperation between industry and academia is possible - albeit difficult - and essential. Two methods for achieving this cooperation are considered. The first is a collection of non-trivial applied mathematical problems of enormous importance to both industry and academia. The second is the establishment of a testbed for rigorous model assessment.

Jean-Pierre Fouque
North Carolina State University
Department of Mathematics
fouque@math.ncsu.edu

“Default and Stochastic Volatility”

We analyze the effects of stochastic volatility on defaults and correlation of defaults.

Lisa Goldberg
MSCI Barra
Department of research
lisa.goldberg@mscibarra.com

“A Top Down Approach to Multi-Name Credit”

We describe a top down approach to forecasting economy-wide defaults and to pricing multi-name credit derivatives from a top down perspective. A self-exciting process is used to model events in the economy and random thinning is used to generate single name default processes.

Ulrich Horst
University of British Columbia
Department of Mathematics
horst@math.ubc.ca

Title and Abstract TBA

David Lando
Copenhagen Business School & Princeton University
Operations Research & Financial Engineering
dlando@princeton.edu

“Decomposing Swap Spreads”

We analyze a six-factor model for Treasury bonds, corporate bonds, and swap rates and decompose swap spreads into three components: A convenience yield from holding Treasuries, a credit risk element from the underlying LIBOR rate, and a factor specific to the swap market. In the later part of our sample, the swap-specific factor is strongly correlated with hedging activity in the MBS market. The model further sheds light on the relationship between AA hazard rates and the spread between LIBOR rates and GC repo rates and on the level of the riskless rate compared to swap and Treasury rates.

Joint work with Peter Feldhütter

Kiseop Lee
University of Louisville
Department of Mathematics
kiseop.lee@louisville.edu

“t-Statistics for Weighted Means in Credit Risk Modelling”

We present a generalization of the two-sample t-test for equality of the means to the case where the sample values are to be given unequal weights. This is a natural situation in financial risk modelling where some samples are considered more reliable than others in predicting a common mean. We describe pooled and unpooled weighted t-tests, and show with an example of real credit data that using the standard unweighted t-test can lead to the poor statistical conclusion.

Randy Miller
Bank of America
Department of Global Portfolio Strategies
randy.j.miller@bankofamerica.com

“Optimal Bank Loan Portfolio Hedging: A Practitioner's Perspective”

Mirela Predescu
University of Toronto
Department of Finance
mirela.predescu01@rotman.utoronto.ca

Monday’s presentation --
“The Valuation of Correlation-Dependent Credit Derivatives Using a Structural Model”

In 1976 Black and Cox proposed a structural model where an obligor defaults when the value of its assets hits a certain barrier. In 2001 Zhou showed how the model can be extended to two obligors whose assets are correlated. In this paper we show how the model can be extended to a large number of different obligors. The correlations between the assets of the obligors are determined by one or more factors. We examine the dynamics for credit spreads implied by the model and explore how the model price tranches of collateralized debt obligations (CDOs). We compare the model with the widely used Gaussian copula model of survival time and test how well the model fits market data on the prices of CDO tranches. We consider two extensions of the model. The first reflects empirical research showing that default correlations are positively dependent on default rates. The second reflects empirical research showing that recovery rates are negatively dependent on default rates.

Tuesday’s presentation --
“The Performance of Structural Models of Default for Firms with Liquid CDS Spreads”

This paper investigates the performance of structural models using a sample of companies with very liquid credit default swap (CDS) contracts. First, I analyze the models’ ability to predict future credit spreads and compare their performance with that of more naïve alternatives that take into account just past CDS spreads. The structural models are implemented in two ways: one is using historical equity data along with balance sheet information to estimate the model, the other is using both equity and past CDS spreads data, in addition to balance sheet information. I find that, on average, a naïve method outperforms the structural models, regardless of their implementation procedure. There is, however, a sub-sample of firm weeks in which the structural models outperform the naïve approach, and these are weeks with significant changes in CDS spreads. Second, I investigate the structural models’ value in predicting credit ratings migrations. I find that long-term changes in the default probabilities implied by structural models have incremental value in anticipating rating downgrades above and beyond CDS spreads changes. However, this is not the case for short-term changes. Over short periods, the incremental information of structural models disappears once I control for CDS spreads.

Thaleia Zariphopoulou
University of Texas at Austin
Department of Mathematics and IROM
zariphop@math.utexas.edu

“Indifference Prices and Stochastic Risk Preferences”

In this talk I will discuss certain aspects of utility based prices related to their behavior across numeraires and investment horizons. I will also analyze the optimal behavior and risk monitoring in the case of stochastic risk preferences. Examples from the Credit Risk area will be presented.

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This page updated on October 25, 2005 3:17 PM