Abstract
This article investigates the joint probability of correlated defaults in the first passage time approach of credit risk subject to condition that the underlying firms’ assets values and the default boundaries follow geometric Brownian motion processes. The exact analytical expression of joint probability of two correlated defaults in the case of stochastic default boundaries is presented. Also, some properties of this solution are provided.
Highlights
Together with the evaluation of loss given default and expected losses of any defaultable financial claim, there is important to estimate the cumulative distribution function of correlated defaults
Default correlation is defined by correlation between the Brownian motions driving the individual companies and plays a crucial role in determining the joint probability of default, i.e. the probability of multiple defaults
Analyzing the credit risk of portfolio, it is important to measure the joint probability of correlated defaults and the general probability of portfolio default
Summary
Together with the evaluation of loss given default and expected losses of any defaultable financial claim, there is important to estimate the cumulative distribution function of correlated defaults. In this paper we analyze the credit risk of portfolio of correlated defaultable claims. One of the most important measures of credit risk, the probability of default of one claim is investigated extensively in the literature. Analyzing the credit risk of portfolio, it is important to measure the joint probability of correlated defaults and the general probability of portfolio default. The correlation between several assets is important for estimating general credit risk of portfolio because higher correlation of defaults implies a greater likelihood that losses will wipe out the assets. Unlike Zhou [1], Patras [7], Overbeck and Schmidt [6] approaches, in this paper we assume that the value of i-th default threshold is stochastic without jumps. The closed form expression of the joint probability of correlated defaults is given in Section 5, and in Section 6 we give some conclusions
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