Determinants of the fair value of debt subject to default risk

Abstract

This thesis contributes to the theory of the fair value of the firm's debt subject to default through structural models of credit risk. The focus has been on four determinants of the firm's debt value:

- the presence of growth opportunities embedded in the firm's assets;

- the lack of perfect information about the firm's assets risk;

- the existence of the implicit option to renegotiate and extend debt maturity;

- the interactions between interest rate risk and default risk.

The main results follow.

When the growth option is exercised so as to maximise equity value, debt value is often higher than when the growth option is exercised so as to maximise the growth option value. Financing the cost of new investment by new subordinated debt rather than by new equity can increase both equity value and senior debt value.

When debt holders are uncertain about the debtor's assets risk (volatility), the cost of borrowing increases and such increases can be very sensitive to the assumed default condition, to the local convexity of the debt value function and to the process the default free short rate is assumed to follow. Assuming high constant assets volatility may not be a prudent assumption when valuing subordinated and subordinated convertible debt in the presence of uncertainty about assets risk. The sensitivity of debt value to (uncertainty about) assets volatility can heavily depend on the stochastic process followed by the default free short interest rate and on the instantaneous correlation between assets value and the short rate.

When, as the firm approaches financial distress, debt maturity can be renegotiated and extended, a valuable "implicit option" to extend debt maturity is present and can significantly alter debt value (and equity value). It is shown that the value of the "extension option" is very sensitive to default conditions and to possible exercise policies. The presence of the "extension option" can increase short-term credit spreads thus improving the predictions of structural models of credit risk.

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