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The option theoretic approach to default considers that the equity holders have a put option on the value of the firms assets, whose strike price is the debt. The rationale is that if the asset value falls below the value of debt, the equity holders are better off by giving the assets to the lenders rather than repaying the debt. The lenders sold the equity holders this option, whose underlying is the firms asset value. This is an option to default when the asset value gets too low. If the asset value drops below that of debt, the liquidation value of the option is the gap, a value gained by stockholders and lost by lenders. This is the option theoretic framework proposed by Merton (1974) (see the fourth section of this chapter).

Hence, when the firm is close to default, the put gains value and the debt value decreases by the put value increase. The more the asset value moves down, the more the put value increases and the less is the value of debt:

Risky debt = risk-free debt — value of the put option

(selling assets at the value of debt)

An economic default occurs when the economic value of assets drops below the value of outstanding debts. Modelling the behaviour of asset value and debt through time allows us to model default. The original Merton model used a fixed amount of debt. Later extensions extended the framework to random debt values driven by the interest rate. However, the current implementation of the Merton model by KMV assumes debt given and certain. Note that an economic default does not imply any legal action and does not coincide with standard legal definitions of default.

Focusing on asset value implies valuing all future flows of the firm, rather than focusing on a single period. The classical corporate finance approach to default is to project future free cash flows to see whether they allow the timely repayment of debt interest and principal. The relevant cash flows are the future free cash flows, or the cash flows from operations left for lenders and equity holders after all economic outflows required to maintain the operating ability of the firm. These future free cash flows should be high enough to face the future debt obligations.

Using the discounted value of free cash flows, which is the firms asset value, is an elegant way of summarizing the information. A short-term view of cash flows is not a relevant criterion for solvency. A temporary shortage of cash does not trigger default as long as there are chances of improvement in the future. Persistent cash flow deficiencies make default highly likely. Temporary deficiencies do not. The market view synthesizes this information. It is consistent with the view of equity as a call option on asset value. As long as there is an upside potential, the equity has value, even during a transitory shortage of cash. The option view of equity serves for pricing the risky debt (Figure 38.1).

KMV Corporation made this framework very popular. The basic scheme above serves to extract from equity prices the default probability of the firm. KMV models default as the event that asset values fall below debt value. This is an economic default, since it does not coincide with the legal definition of default. KMV calls the default point the value of asset equal to debt. The probability of this event results from the asset value distribution and from the debt value. It is an implied default probability that the KMV Corporation names the Edf. The Credit Monitor model, from KMV Corporation, implements this framework to extract the Edf from observable equity price data. The Edf is forward looking, unlike historical data, because equity prices are forward looking.

Implementing this framework raises difficulties and needs simplification. KMV models default at a given horizon, where the asset value is above or below the debt value. The debt value combines short-term debt plus a fraction of long-term debt. Real situations are more complex. Another technical difficulty is to extract the asset values and distribution characteristics from observable data. The next section addresses this issue.

using numerical calculations, although these equations are implicit functions A₀ and a (A). However, this simplified model is not sufficient to reconstruct the KMV Edf, since it bypasses the calibration process with actual default data.