(Joint work with with Bianca Hilberink)

Abstract:

In a sequence of fascinating papers, Leland and Leland & Toft have
investigated various properties of the debt and credit of a firm which
keeps a constant profile of debt and chooses its bankruptcy level
endogenously, to maximise the value of the equity. One
feature of these papers is that the credit spreads tend to zero as
the maturity tends to zero, and this is not a feature which is
observed in practice. This defect of the modelling appears to
be related to the diffusion assumptions made in the papers
referred to; in this paper, we take a model for the value of
the firm's assets which allows for jumps, and find that the
spreads do not go to zero as maturity goes to zero. The modelling
is quite delicate, but it just works; analysis takes us a long
way, and for the final steps we have to resort to numerical
methods.