Intensity-Based Valuation of Defaultable Claims

Abstract

As already mentioned in Sect. 1.4, existing approaches to the modeling of credit (or default) risk may be divided into two broad classes: structural models and reduced-form models. In the former approach, the total value of the firm’s assets is directly used to determine the default event, which occurs when the firm’s value falls through some boundary. It results that here the default time is a predictable stopping time with respect to the reference filtration modeling the information flow available to the traders. This means that the random time of default is announced by an increasing sequence of stopping times. By contrast, in the latter approach, the firm’s value process either is not modeled at all, or it plays only an auxiliary role of a state variable. The default time is modeled as a stopping time that is not predictable; the default event thus arrives as a total surprise. Formally, the random time of default event is given here as a totally inaccessible stopping time, in the terminology of the general theory of stochastic processes (see, e.g., Dellacherie (1972) or Jacod and Shiryaev (1987)). The main tool in this approach is an exogenous specification of the conditional probability of default, given that default has not yet occurred. Since in most cases this is done by means of the hazard rate (or intensity) of default, reduced-form models are also commonly known as hazard rate models or intensity-based models. From a long list of papers devoted to the reduced-form methodology, let us mention a few: Artzner and Delbaen (1995), Jarrow and Turnbull (1995), Duffle et al. (1996), Duffle and Singleton (1997, 1999), Lando (1998), Schlögl (1998), Schönbucher (1998b), Wong (1998), Elliott et al. (2000), and Bélanger et al. (2001).KeywordsPrice ProcessContingent ClaimCorporate BondCredit SpreadSaving AccountThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.