Default risk, asset pricing and debt control

L. Grüne, W. Semmler: Default risk, asset pricing and debt control
Journal of Financial Econometrics 3, 79 - 106, 2005

DOI: 10.1093/jjfinec/nbi006
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The pricing and control of firms' debt has become a major issue since Merton's (1974) seminal paper. Yet, Merton as well as other recent theories presume that the asset value of the firm is independent of the debt of the firm. However, when using debt finance firms may have to pay a premium for an idiosyncratic default risk and may face debt constraints. We demonstrate that firm specific debt constraints and endogeneous risk premia, based on collateralized borrowing, affect the asset value of the firm and, in turn, the collateral value of the firm. In order to explore the interdependence of debt finance and asset pricing of firms we endogenize default premia and borrowing constraints in a production based asset pricing model. In this context the dynamic decision problem of maximizing the present value of the firm faces an additional constraint giving rise to the debt dependent firm value. We solve for the asset value of the firm with debt finance by the use of numerical dynamic programming and set valued numerical techniques. This allows us to solve the debt control problem and to compute sustainable debt as well as the firm's debt value.

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