A Structural Model with Unobserved Default Boundary
by Thorsten Schmidt of the University of Leipzig
October 9, 2006
Abstract: We consider a firm-value model similar to the one proposed by Black and Cox (1976) where additionally the firm value is allowed to jump and instead of assuming a constant and known default boundary, the default boundary is a random and unobserved process. This process has a Brownian component, reflecting the influence of uncertain effects on the precise timing of the default, and a jump component, which relates to abrupt changes in the policy of the company, exogenous events or changes in the debt structure. Interestingly, this setup admits a default intensity, so the reduced form methodology can be applied. We examine consequences for the relationship between equity and debt and consider the pricing of equity default swaps.
Keywords: structural model, equity default swaps, default boundary, jump-diffusion.
Published in: Applied Mathematical Finance, Vol. 15, No. 2, (April 2008), pp. 183-203.
Previously titled: A Structural Model with Random Default Boundary