Multiscale Intensity Models and Name Grouping for Valuation of Multi-Name Credit Derivatives

Abstract

Abstract. The pricing of collateralized debt obligations and other basket credit derivatives is contingent upon (i) a realistic modeling of the firms' default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the individual firms' default time distributions. Factor models, a widelyused class of pricing models, are computationally tractable despite the large dimension of the pricing problem, thus satisfying issue (ii), but to have any hope of calibrating CDO data, numerically intense versions of these models are required. We revisit the intensity-based modeling setup for basket credit derivatives and, with the aforementioned issues in mind, we propose improvements (a) via incorporating fast mean-reverting stochastic volatility in the default intensity processes, and (b) by considering homogeneous groups within the original set of firms. This can be thought of as a hybrid of top-down and bottom-up approaches. We present a calibration example, including data in the midst of the 2008 financial credit crisis, and discuss the relative performance of the framework.

Utility valuation of multi-name credit derivatives and application to CDOs

“…The holder of a CDO tranche insures losses due to defaults between certain bounds (the attachment points characterizing the tranche). For some other approaches based on arbitrage pricing using intensity-based or copula models, we refer, for instance to [8,10,11,17,18,20,28]. A multi-dimensional structural model for loss distributions is studied in [14].…”

“…Recall that for the tranche holder receiving a premium at rate Re rt at time t on his remaining notional, the wealth dynamics are given by (28). When there are n firms alive, the value function, denoted by H (n) (t, x, y) satisfies…”

“…For N = 25 firms, the results are shown in Figure 4. Intensity-based arbitrage pricing is studied in [11,27,28], where it is demonstrated in a variety of models that it is difficult to fit the market-quoted senior tranche spread without overstating enormously the mezzanine tranches. As Figure 4 shows, these are better captured with utility valuation that reflects the specialization and relative illiquidity of the market in these derivatives.…”

Multiname and Multiscale Default Modeling

“…The main drawback of this approach is the fact that these are static models which do not take into account the time evolution of joint default risks. This has been recognized in the academic literature on dynamic models with recent developments in the multiname structural approach [10,13], reduced form models [2,16,15,4], and top-down models [6,14,18].…”

Computational techniques for basic affine models of portfolio credit risk

“…Due to the rapid growth of the market for credit derivatives over the past decade, intensity-based models of credit risk are currently an active area of research. See for example Duffie and Gârleanu (2001), Giesecke and Goldberg (2005), Errais, Giesecke, and Goldberg (2006), Joshi and Stacey (2006), Mortensen (2006), Papageorgiou and Sircar (2008), and Longstaff and Rajan (2008). In our analysis we rely heavily on the doubly stochastic assumption for default intensities, so that correlation of default intensities is the only mechanism by which correlation of default times can arise.…”