Our aim is to give a theoretical study for the modelling of default risk. We provide first a detailed analysis of the relatively simple case when the flow of informations available to an agent reduces to the observations of the random time which models the default event. Subsequently, the case of the general filtration is examined. The focus is on the evaluation of conditional expectations with...

We consider the problem of modelling the term structure of bonds subject to default risk, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of default at predictable times. It turns out that this requires the introduction of an additional term to the forward-rate approach by Heath, Jarro...

This paper provides an alternative approach to Duffie and Lando [7] for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by constructing an economy where the market sees the manager’s information set plus noise. The noise makes default a surprise to the market. In contrast, we obtain a reduced form model by constructing an economy ...

We apply the density framework developed in [N. El Karoui, M. Jeanblanc, and Y. Jiao, Stochastic Process. Appl., 120 (2010), pp. 1011–1032] to the modeling of successive multiple defaults. Under the hypothesis of existence of the joint density of the ordered default times with respect to a reference filtration, we present general pricing results and establish links with the classical intensity ...

In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swa...

We present an intensity-based model of correlated defaults with application to the valuation of defaultable securities. The model assumes that the conditional hazard rate of default is driven by external common factors as well as other defaults in the system. A proposed recursive procedure can be used to generate default times with a broad class of correlation structures. We compare this approa...

A thorough understanding of the joint default behavior of credit-risky securities is essential for credit risk measurement as well as the valuation of multi-name credit derivatives and Collateralized Debt Obligations. In this paper we study a simple and tractable intensity-based model for correlated defaults, in which unpredictable default arrival times are jointly exponentially distributed. Si...

∗This work was completed during our visit to the Isaac Newton Institute for Mathematical Sciences in Cambridge. We thank the organizers of the programme Developments in Quantitative Finance for the kind invitation. †The research of T.R. Bielecki was supported by NSF Grant 0202851 and Moody’s Corporation grant 5-55411. ‡The research of M. Jeanblanc was supported by Zéliade, Itô33, and Moody’s Co...

We consider a firm-value model similar to the one proposed by Black and Cox (1976) where additionally the firm value is allowed to jump and instead of assuming a constant and known default boundary, the default boundary is a random and unobserved process. This process has a Brownian component, reflecting the influence of uncertain effects on the precise timing of the default, and a jump compone...

This paper employs non-parametric specification tests developed in Hong and Li (2005) to evaluate several one-factor reduced-form credit risk models for actual default intensities. Using estimates for actual default probabilities provided by Moody’s KMV from 1994 to 2005 for 106 U.S. firms in seven industry groups, we strongly reject popular univariate affine model specifications. As a good com...