Effects of economic interactions on credit risk

Abstract

Abstract. We study a credit risk model which captures effects of economic interactions on a firm's default probability. Economic interactions are represented as a functionally defined graph, and the existence of both cooperative, and competitive, business relations is taken into account. We provide an analytic solution of the model in a limit where the number of business relations of each company is large, but the overall fraction of the economy with which a given company interacts may be small. While the effects of economic interactions are relatively weak in typical (most probable) scenarios, they are pronounced in situations of economic stress, and thus lead to a substantial fattening of the tails of loss distributions in large loan portfolios. This manifests itself in a pronounced enhancement of the Value at Risk computed for interacting economies in comparison with their non-interacting counterparts.

Credit contagion and credit risk

“…2 and 3. We note that the tails of the loss-frequency distribution and the loss distribution are more pronounced than in our previous study [11]. This solely due to the fact that in the present paper we followed the Basel II suggestion that relates the coupling of a company to macro-economic factors with its default probability via (4).…”

“…We have not looked specifically at finite size effects here. In [11] it was shown that they are fairly small. …”

“…In this way, the contribution to the total losses will be approximately uniform over the bands of different default probabilities. The distribution of the economy-wide losses per node is driven by the distribution of the macro-economic factor, and is computed analytically as shown in [11]. A typical result is shown in Fig.…”

“…From a reduced form point of view this is just the intensity of default of firm i at time step t (in a given economic environment specified by the set of firms defaulted at time t). This allows us to re-interpret the (rescaled) initial wealth and impact variables ϑ i and J ij in terms of the bare default probabilities [11,12,13]. I.e., if company i has an expected default probability of p i in a given time unit (e.g.…”

Volatility Effects on the Escape Time in Financial Market Models

“…In SVMs the volatility is changing randomly according to some stochastic differential equation or some discrete random processes. Recently, models of financial markets reproducing the most prominent statistical properties of stock market data, whose dynamics is governed by non-linear stochastic differential equations, have been proposed [Malcai et al, 2002;Borland, 2002;Borland, 2002b;Hatchett & Kühn, 2006;Bouchaud & Cont, 1998;Bouchaud, 2001;Bouchaud, 2002;Sornette, 2003;Bonanno et al, 2006;Bonanno et al, 2007].…”