BSLP: Markovian bivariate spread-loss model for portfolio credit derivatives

Abstract

BSLP is a two-dimensional dynamic model of interacting portfolio-level loss and loss intensity processes. It is constructed as a Markovian, short-rate intensity model, which facilitates fast lattice methods for pricing various portfolio credit derivatives such as tranche options, forward-starting tranches, leveraged super-senior tranches etc. A semiparametric model specification is used to achieve near perfect calibration to any set of consistent portfolio tranche quotes. The one-dimensional local intensity model obtained in the zero volatility limit of the stochastic intensity is useful in its own right for pricing non-standard index tranches by arbitrage-free interpolation.Opinions expressed in this paper are those of the authors, and do not necessarily reflect the view of JP Morgan. We would like to thank for valuable discussions. All remaining errors are our own. arXiv:0901.3398v1 [q-fin.PR]

Hedging default risks of CDOs in Markovian contagion models

“…Intensities depending upon the number of defaults are related to mean-field approaches (see Frey & Backhaus (2006) . This is discussed in van der Voort (2006), Arnsdorf & Halperin (2007) or Lopatin & Misirpashaev (2007). Later on, we provide a calibration procedure of such unconstrained intensities onto market inputs such as expected losses on CDO tranches.…”

“…Such ideas have been put in practice by Arnsdorf & Halperin (2007), de Koch & Kraft (2007), Herbertsson (2007), Lopatin & Misirpashaev (2007) and Herbertsson & Rootzén (2006) for the pricing of basket credit derivatives and also with respect to calibration issues.…”

Pricing credit derivatives under incomplete information: a nonlinear-filtering approach

“…In Section 4.1 we derive a finite dimensional filtering algorithm (Algorithm 4.3) for the case where the pair process (X, Y) follows a finite state Markov chain. Models of this type are frequently being used in portfolio credit risk modelling (with observable X); examples include the infectious defaults model discussed in Section 2.3 or the Markov-chain models of Arnsdorf & Halperin (2007) and of Frey & Backhaus (2007). Moreover, the results for the finite state Markov case can be used to construct a filter approximation for general jump-diffusion models, as will be shown in Section 5 below.…”

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

“…In order to circumvent this issue, the usual way is to relax some assumptions, such as constant correlation, Brownian increments in asset prices, introducing some clustering effects through 3 For instance, some academics tend to think that the use of a Gumbel, Clayton or a t-copula would have avoided the pitfalls of the Gaussian copula approach. We refer to Burtschell et al (2009), Cousin and Laurent (2008a), Cousin and Laurent (2008c) or Gregory and Laurent (2008) for reviews of a number of popular pricing approaches.…”

“…They show some robustness of the Gaussian copula approach. 21 Backhaus (2007, 2008), Arnsdorf and Halperin (2007) provide some Markovian loss models which are more versatile, but also more difficult to handle. 22 We might have alternatively considered the Gaussian copula as a (non Markovian) contagion model.…”