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Programme
Marek RUTKOWSKI (Université de Varsovie)
Hedging of default-free and defaultable derivatives: a critical overview.
A large number of papers devoted to the modelling of credit/default risk and the valuation of credit-risk-sensitive contingent claims were published in recent years. However, the important issue of producing efficient and easy to implement hedging strategies is still lacking a widely accepted solution. This deficiency seems to be at least partially due to the way in which typical models of credit risk are constructed. The goal of the talk is to analyze existing approaches to financial modelling from the perspective of identification and hedging of risks (including credit risk).
Texte des transparents disponible (format pdf).
Farshid JAMSHIDIAN (NIB Capital)
Credit default swap and swaptions
This paper presents a conceptual framework for valuation of single-name credit derivatives, and recuperates, in some cases generalizing, a few of known results in credit risk theory. Valuation is viewed with respect to a given state price density and relative to a general numeraire. Survival probabilities and default recoveries are considered as processes adapted to a subfiltration, following Jeanblanc and Rutosksy [JR], or, in the special case of Cox processes, Lando [L]. A result of Duffie and Singleton [DS] on pricing bonds with recovery in terms of loss ratio is reproduced. The notion of coadapted change of numeraire is introduced, and its invariants identified and studied. The concept of a credit claim is formalized by introducing notions of $T$-claims, $\tau$-claims, and $\T$-streams. Application is made to credit default swaps and swaption, and the latter is approximated by a Black-Scholes formula due to Schönbucher[S]. Texte et transparents disponibles (format pdf).
Hugues PIROTTE (Solvay Business School, Bruxelles) A Structural Model of the Term Structure of Credit Spreads with Stochastic Recovery and Contractual Design
This paper presents an alternative modelling of the term structure of the credit spreads under a structural approach. We rely upon the barrier option pric-ing framework to price a corporate zero-coupon bond with a stochastic present value of the recovery consistent with the evidence on the business cycle effects. Stochastic interest rates are therefore introduced through a two-factor model of the term structure of interest rates that impacts the assets value of the firm. Comparative statics with similar models such as Briys and de Varenne [1997] are provided thereafter. The pricing model is then shown to be related to the corporate context of an external funding requirement of an investment project leading to endogenous values of the dividend payout rate and the default thresh-old value. Finally, the asset volatility, which accounts for much of the credit risk in this class of models, is related to the stock market volatility through a backward use of the model therefore adding to its tractability while taking advantage of the liquidity and information dissemination in stock markets.
Texte des transparents disponible (format ppt - PowerPoint).
Jean Paul LAURENT (BNP Paribas et Université de Lyon) Basket default swaps, CDO's and factor copulas
We consider a factor copula approach to the pricing of basket credit derivatives and CDO tranches. Our purpose is to deal in a convenient way with dependent defaults aand credit spreads. We provide semi-explicit expressions of the stochastic intensities of default times, credit spreads and price of basket default swaps involving large number of names. We also consider the explicit pricing of CDO tranches within our framework. Two cases are studied in detail : mean variance mixxtire structure models and Archimedean copulas. Texte disponible (format pdf).
Jean-Frédéric JOUANIN (Crédit Lyonnais)
Modelling Dependence for Credit Derivatives with Copulae
An important issue when pricing a basket credit derivative is to retrieve the joint probability distribution of the collection of the firms' default times. The problem is trivial when default times are assumed to be independent. But it is well known among market practitioners that such an hypothesis does not allow to fit the observed prices of simple multi-asset products such as first-to-defaults. But when one wants to weaken this assumption the problem becomes much more intricate.
One method is first to estimate the marginal probability distribution of each individual default and then to use copulae to model the joint distribution. We will first recall the commonly-used intensity-based (or reduced-form) framework, in which a default event is said to occur when a known hazard process exceeds an unobserved threshold random variable. Then, two main approaches will be considered: the first one consists in modelling directly the joint survival function of default times (Li), whereas in the second approach, we only link the threshold random variables with a copula (Schönbucher & Schubert, Giesecke). We will compare these two approaches and give some results about their relationships. Then, we give an example of the pricing method with the valuation of first-to-defaults or more sophisticated products like collateralized debt obligations. Finally, we discuss the problem of the choice of the copula family (Gaussian, Student, or else) and the possible calibration of the parameter of the copula on market spread jumps. Transparents disponibles (format pdf).
Kay GIESECKE (Department of Operations Research and Industrial Engineering, Cornell University) Credit Contagion and Aggregate Losses
Credit contagion refers to the propagation of economic distress from one firm or sovereign government to another. In this paper we model credit contagion phenomena and study the fluctuation of aggregate credit losses on large portfolios of financial positions. The joint dynamics of firms' credit ratings is modeled by a voter process, which is well-known in the theory of interacting particle systems. We clarify the structure of the equilibrium joint rating distribution using ergodic decomposition. We analyze the quantiles of the portfolio loss distribution and in particular their relation to the degree of model risk. After a proper re-scaling taking care of the heavy tails induced by the contagion dynamics, we provide a normal approximation of both the equilibrium rating distribution and the portfolio loss distribution. Texte et transparents disponibles (format pdf).
Philip SCHOENBUCHER (ETH, Zurich) Modelling dynamic portfolio credit risk
In this paper we present a continuous-time portfolio credit risk model which allows a closed-form evaluation of (i) the price dynamics of the defaultable bonds, and (ii) the joint default survival and default probabilities
The specification of the default dependency is based upon a generalisation of the Archimedean Copula class in form of a factor model which allows a high degree of flexibility in the specification of (nonnegative) pairwise default dependencies.
