An extension of Davis and Lo's contagion model

Abstract

: The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo's infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by not necessarily independent Bernoulli-type random variables. Moreover, several contaminations could be required to infect another firm. In this paper we compute the probability distribution function of the total number of defaults in a dependency context. We also give a simple recursive algorithm to compute this distribution in an exchangeability context. Numerical applications illustrate the impact of exchangeability among direct defaults and among contaminations, on different indicators calculated from the law of the total number of defaults. We then calibrate the model on iTraxx data before and during the crisis. The dynamic feature together with the contagion effect have a significant impact on the model performance, especially during the recent distressed period.

Estimating the probability of multiple EU sovereign defaults using CDS and bond data

“…. , 1 N (t k , t k+1 ) follows a multivariate binomial distribution (see Davis and Lo [2001], Cousin et al[2012]) with correlation equal to R(t k , t k+1 ):…”

A dynamic approach merging network theory and credit risk techniques to assess systemic risk in financial networks

“…For analysing a systemic crisis we found that T = 7 years is a reasonable choice. The contagion mechanism is particularly intuitive and simple: the default of one node increases the probability of default of the neighbouring nodes in subsequent time steps [44][45][46][47] according the characteristics of the network of exposures {a ij }. In particular, a node i experiences an impact I i (t) at time t:…”

Moment estimates in the first Borel-Cantelli Lemma with applications to mean deviation frequencies

“…Very recently, we learned of the results in [3], where the idea of studying the decay of ∞ m=n P(E m ) combined with metastability appears, although not in the context of a systematic study of the moments of O. Moreover, recent applications of the overlap statistic, which include the Schutte-Nesbitt formula and moments of the overlap statistic in special cases, are found in information theory and finance [4,5,17]. In the probability textbooks the Borel-Cantelli Lemmas appear essentially unchanged without taking advantage of the fine information in the Schuette-Nesbit formula [30], see for example [6,11,21,26,35,36,47].…”