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Timetable (DQFW04)

Industry Event: Credit

Friday 25th February 2005 to Saturday 26th February 2005

Friday 25th February 2005
09:30 to 10:00 Coffee
10:00 to 11:00 Stochastic network methods in portfolio credit risk

Modelling the default performance of a large heterogeneous portfolio is a major topic in credit risk. One approach is to derive analytic or partly analytic approximations based on the law of large numbers and/or central limit theorem; examples are Vasicek’s large homogeneous portfolio model or the saddle point approximations used in CreditRisk+. Here we introduce an approach based on ideas from stochastic networks. The portfolio members are thought of as particles that move around a number of credit risk states (credit ratings) before eventually defaulting. The transition rates are supposed to depend on an external ‘environment’ process, thus introducing dependence between the particles. We study the limiting behaviour of this system as the number of particles increases, obtaining conditional fluid and diffusion limits from which portfolio performance can be predicted.

11:00 to 12:00 The gaussian copula model and beyond

The Gaussian copula model has become an industry standard in the pricing of multi-name credit derivative products. Whilst the model has highly questionable dynamics, it has given the theoretical foundations for a huge growth in credit correlation products over the last few years. We describe the current situation regarding the use of this model and highlight some of the challenges currently faced by practitioners such as parametrisation, efficient calculation of greeks and modelling of the correlation skew.

12:00 to 13:30 Lunch
13:30 to 14:30 Hedging Credit Risk: theory and practice

We discuss recent theoretical progress in hedging and managing credit risk together with issues of practical implementation with respect to specific products.

14:30 to 15:30 Matching base correlation skew with a naturally time-homogeneous model

We introduce a new financially motivated model for pricing portfolio credit derivatives. It naturally matches the base correlation skew whilst achieving time-homogeneity; two features lacking in the market-standard Gaussian copula model. The model is easily calibrated and allows effective pricing of exotic credit derivatives such as CDO-squareds.

15:30 to 16:00 Tea
16:00 to 17:00 Dependent defaults and changes of time

We propose a dynamic multi-name credit model framework based on time changed point processes. At the center of our approach is the sequence of unpredictable defaults and losses, which we represent as a rescaled marked Poisson process. We construct the stochastic time change through the compensator of the default counting process. This yields algorithms for the simulation of dependent defaults and losses that start with a simple Poisson sequence. The dynamics of dependent defaults are governed by the evolution of observable information. Specific information structures lead to the known multi-name models and a great deal more. We characterize a new class of flexible self-exciting default processes as time-changed Poisson processes. Applications include the pricing and risk management of multi-name credit products such as basket CDS, CDO's and tranches.

17:00 to 18:00 A McNeil (ETH Zürich)
Statistical inference for dependent default and dependent migration models

Any portfolio credit risk model that is to be used to calculate a loss distribution associated with defaults and changes in rating must address the challenge of modelling dependent defaults and dependent rating migrations. Most industry models (such as KMV, CreditMetrics, CreditRisk+) incorporate mechanisms for modelling this dependence, generally by assuming conditional independence of defaults and migrations given common economic factors. However, the calibration of these mechanisms is often quite ad hoc, despite the fact that the tail of the portfolio loss distribution is extremely sensitive to small changes in the parameters governing dependence.

We consider the problem of making formal statistical inference for such models based on historical default and rating migration data. In the solution we propose portfolio credit models are represented as generalized linear mixed models (GLMMs) and inference is made using Markov chain Monte Carlo (MCMC) techniques. This general framework allows quite complex models with a latent random effects structure to represent unobserved common factors that influence default and migration.

18:00 to 19:00 Wine and beer reception
Saturday 26th February 2005
08:30 to 09:30 Modelling correlation skew via mixing copulae and uncertain loss at default (Venue: Centre for Mathematical Sciences)

We discuss aspects of the correlation skew in portfolio credit derivatives, in particular the relationship between implied and base correlation for tranches. We present a model which generates correlation skews by mixing copulae and introducing stochastic loss given default variables. This allows us to present a whole range of arbitrage-free base correlation curves.

09:30 to 10:30 Pricing of basket default swaps and CDO tranches Venue: Centre for Mathematical Sciences

The choice of a dependence structure between default times drives the prices of basket default swaps and CDO tranches. We therefore assess the model risk associated with the pricing of multiname credit derivatives. We discuss the comparison methodology and consequently we consider different pricing models associated with different copulas of default times: Gaussian, Student t, Clayton, Marshall-Olkin, double t. We emphasize the use of stochastic orders to derive some properties of CDO tranche premiums. It can be shown that base correlation tranches premiums increase with some dependence parameters. We also compare semi-explicit pricing approaches and the use of large portfolio approximation techniques.

10:30 to 11:00 Coffee Venue: Centre for Mathematical Sciences
11:00 to 12:00 Extensions of the gaussian copula Venue: Centre for Mathematical Sciences

With the dual pourpose of investigating short-comings of the Gaussian copula model and of modelling the correlation "skew" observed in the CDO market, we describe extensions to the Gaussian copula model which incorporate random recovery and random (level dependent) factor loadings, respectively. We discuss the calibration of these new models and their respective impact on CDO tranche prices. The main conclusion is that when properly calibrated, the random recovery extension does not give rise to a significant skew, whereas the random factor loading model can generate a wide range of skews, including those observed in the market.

12:00 to 13:30 Lunch Venue: Centre for Mathematical Sciences
13:30 to 14:30 The pricing of options on individual CDS and CDS indices Venue: Centre for Mathematical Sciences

While options on single-name CDS can be priced quite efficiently by using the "survival measure" to remove all explicit reference to the obligor's default risk, the pricing of options on CDS indices pose some new, interesting challenges to the credit risk modeller. Essentially, options on CDS indices require the formulation of a dynamic default dependency model on the whole underlying credit index. In this paper we discuss the possibility of pricing such options using frailty models of default dependency and furthermore analyse the extent to which survival-measure based techniques can be used to find approximate option prices.

14:30 to 15:30 Valuing CDOs Venue: Centre for Mathematical Sciences
15:30 to 16:30 Tea Venue: Centre for Mathematical Sciences
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons