Large portfolio losses: A dynamic contagion model

Abstract

Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the “Central Limit Theorem” useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis

The role of disorder in the dynamics of critical fluctuations of mean field models

“…Even if the mean field hypothesis may seem too simplistic to describe physical systems, where geometry and short-range interactions are involved, mean field models have been recently applied to social sciences and finance, as in [3,8,9,11,14,16]. The advantage of dealing with this kind of models is that they usually are analytically tractable and it is rather simple derive their macroscopic equations.…”

Social interaction and conformism in a random utility model

“…In Section 2 we present our dynamic version of a random utility model with conformism. In Section 3 we analyze a continuous time dynamical system relying upon results obtained in Dai Pra et al (2009) specifying the different settings for conformism evolution and we characterize the stationary equilibria of the model. In Section 4 we provide comparative statics for the different models.…”

Heterogeneous credit portfolios and the dynamics of the aggregate losses

“…In most cases, these dynamical fluctuation theorems are proved by the method of weak convergence of processes; this approach has been widely applied to models close in spirit to this work. We quote [4,6] for applications to finance. The effectiveness of those methods for heterogeneous models is, however, unclear.…”

“…In the risk management context, our model may be useful for the management of large portfolios, in the spirit of other models proposed in [10] or in [6]. It has been remarked that in many real world applications defaults are rather rare events, with the result that, for instance, the fraction of defaulted firms is close to zero and a normal approximation is not meaningful.…”

“…On the other hand, to our knowledge, this is the first attempt to apply large deviations and normal fluctuation theory on path spaces (that is, in a dynamic fashion) for finance or credit management purposes, except for what is contained in [6]. Moreover, the model studied in [6] did not require the development of large deviations in Banach spaces as we are forced to use here. For a survey on more standard non-dynamic large deviation methods applied to finance and credit risk see [11].…”