Seminar: Winter 2003

Amir Dembo & Darrell Duffie

We use large-deviations methods to analyse the tail risk of losses on large insurance or bank portfolios. Among other results, we calculate the approximate contribution to large tail losses of each type of position, as an input to portfolio structuring decisions. We provide conditions under which a portfolio lifetime risk measure can be reduced to a measure similar to value at risk. Based on joint work with Jean-Dominique Deuschel
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Zhifeng Zhang (Morgan Stanley)

In this talk, we will carry out the natural development path of loan pricing models. We explore the relationship between loan, bond, and the default swap market under the assumptions that the draw/prepayment amount is given at value date. We propose an optimal control framework to evaluate the embedded options and illustrate a dynamic programming technique to implement it. A brief overview of the credit derivative market is presented at the beginning of the talk.
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Gerald Fahner

Statistical methods can be of enormous value to improve and optimize the behavior of complex systems, such as chemical plants, or consumers' usage of credit cards. I will give an overview over current testing practices used by many lenders/marketers for the crucial task of improving response rates and profitability from credit offers, and point out some problems and inefficiencies associated with these approaches. I will describe how more elaborate statistical methods of experimental design and regression analysis can reap additional benefits of faster learning and increased confidence in performance estimates and optimization results. I will discuss how some unique business- and operational constraints in this industry can be tackled by searching for constrained optimal experimental designs, and illustrate this approach with case study results.
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Peter Carr (Courant Institute, NYU)

Option pricing has been literally transformed since the introduction of harmonic analysis in the early 90's. This talk focuses on the use of Fourier transforms in pricing European options.

We emphasize models of the underlying asset dynamics which simultaneously account for jumps, stochastic volatility, and the leverage effect.
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Dilip Madan (University of Maryland)

Infinite activity Levy processes are introduced as synthesizing processes for asset returns, both in their statistical and risk neutral incarnations.

The successes are noted and the failures described. Measure change puzzles are resolved and modeling issues facing the industry are enumerated.
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Francis Longstaff (UCLA)

We study the optimal recursive refinancing problem where a borrower minimizes his lifetime mortgage costs by repeatedly refinancing when rates drop sufficiently. Key factors affecting the optimal decision are the cost of refinancing and the possibility that the mortgagor may have to refinance at a premium rate because of his credit. The optimal recursive strategy often results in prepayment being delayed significantly relative to traditional models. Furthermore, mortgage values can exceed par by much more than the cost of refinancing. Applying the recursive model to an extensive sample of mortgage-backed security prices, we find that the implied credit spreads that match these prices closely parallel borrowers' actual spreads at the origination of the mortgage. These results suggest that optimal recursive models may provide a promising alternative to the reduced-form prepayment models widely used in practice.
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Jim Gatheral (Merrill Lynch)

We show how stochastic volatility models relate to a simple market microstructure model and investigate further implications of this model for the impact of large option trades on the implied volatility surface.
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Lisa Goldberg (BARRA)

We develop a structural model of default risk that incorporates the short-term uncertainty inherent in default events. It is based on the assumption of incomplete information: We take as a premise that bond investors are not certain about the true level of firm value that will trigger default.

The coherent integration of structure and uncertainty is facilitated with compensators. Compensators form the infrastructure of a class of credit models that is broad enough to include traditional structural models, intensity-based models and a great deal more.

We give several empirical examples that compare default probabilities and credit yield spreads forecast by our compensator model to the output of a Black & Cox (1976) model. We find that our compensator model reacts more quickly and, unlike traditional structural models, forecasts positive short-term credit spreads for firms that are in distress.

We conclude by demonstrating the curious and thought-provoking fact that, while our model is predicated on the surprise nature of default, it does not admit a conditional default rate.
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