Firm value, diversified capital assets, and credit risk: towards a theory of default correlation

Willi Semmler, Lucas Bernard, Lars Grüne

Abstract

ABSTRACT

Following the lead of Merton (1974), recent research has focused on the relationship of credit risk to firm value. Although this has usually been done for a single firm, the growth of structured finance, which necessarily involves the correlation between included securities, has spurred interest in the connection between credit default risk and the dependencies and cross-correlations arising in families of firms. Previous work by Grüne and Semmler (2005), focusing on a single firm, has shown that firm-value models, incorporating company-specific endogenous risk premia, imply that exposure to risk does impact asset value. In this paper, we extend these results to study the effects of random shocks to diversified capital assets, wherein the shocks are correlated to varying degrees. Thus, we construct a framework within which the effects of correlated shocks to capital assets can be related to the probability of default for the company. The dynamic decision problem of maximizing the present value of a firm faced with stochastic shocks is solved using numerical techniques. Further, the impact of varying dependency structures on the overall default rate is also explored.