This article presents a tractable structural model in which default may be both expected or unexpected. The model can predict realistically high short-term credit spreads. Closed form solutions are provided for corporate bonds and default swaps. The analysis suggests that, in order for the observed short-term yield spreads on high grade corporate debt to be compensation for credit risk, the market must believe that unexpected default may occur at any time, even if it is extremely unlikely, and that it may cause a dramatic sudden 'downfall' in the firm's assets value.
This paper tests a¢ ne, quadratic and Black-type Gaussian models on Euro area triple A Government bond yields for maturities up to 30 years. Quadratic Gaussian models beat a¢ ne Gaussian models both in sample and out of sample. A Black-type model best …ts the shortest maturities and the extremely low yields since 2013, but worst …ts the longest maturities. Even for quadratic models we can infer the latent factors from some yields observed without errors, which makes quasi maximum likelihood (QML) estimation feasible. New speci…cations of quadratic models …t the longest maturities better than does the "classic" speci…cation of Ahn-Dittmar-Gallant (2002), but the opposite is true for the shortest maturities. These new speci…cations are more suitable to QML estimation. Overall quadratic models seem preferable to a¢ ne Gaussian models, because of superior empirical performance, and to Black-type models, because of superior tractability. This paper also proposes the vertical method of lines (MOL) to solve numerically partial di¤erential equations (PDE's) for pricing bonds under multiple non-independent stochastic factors. "Splitting" the PDE drastically reduces computations. Vertical MOL can be considerably faster and more accurate than …nite di¤erence methods.
This paper presents a tractable structural model whereby controlling equity holders are also among the creditors of the firm. As the firm approaches distress, equity holders can drain the assets of the firm and expropriate other creditors by repaying their credit before bankruptcy. The right of the bankruptcy court to revoke such repayment protects arm's length creditors, reduces the cost of borrowing and induces equity holders to anticipate repayment of their credit. Equity holders decide repayment neither too early nor too late, so as to reduce the risk of repayment revocation by the bankruptcy court. Similar conclusions apply to the preferential repayment of bank loans personally guaranteed by equity holders. The analysis also suggests that callable bearer bonds may be more valuable to equity holders than to other creditors. Copyright 2007 The Authors Journal compilation (c) 2007 Blackwell Publishing Ltd.
This article presents, estimates and tests a credit default swap (CDS) pricing model, which links a firm's default intensity to its observed stock price. The pricing model requires finite difference numerical solutions. In spite of this quasi-maximum likelihood parameter estimation is still feasible. Evidence from a sample of large corporations confirms the validity of the link between the firm's stock price and default intensity.
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