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Some variations of Mertons model existed before 1974, implying default when asset value goes under a preset value of debt, and others are extensions, progressively extending the scope of the model to other variables.

The gamblers ruin model considers that a gambler plays with a cash reserve from which he pays negative payoffs and to which positive payoffs are added. Wilcox (1971, 1973) considers the cash flow to have any one of two values at each gamble. The cash reserve is the equity of the firm. Default occurs when the cash drops to zero. Others have extended the model⁵. In this case, the equity has a preset value, which does not recognize the fact that a firm does not fail simply because it runs out of cash. Firms have upside potential from further opportunities that make the equity market value closer to the economic reality than the book value.

The rationale of relating default probability to observable attributes is not far from the equity cash reserve model. For instance, when looking at the ability to face debt obligation through interest coverage ratios, we get close to the view of an exhausting cash reserve with negative cash flows. If interest coverage ratios get below 1, the firm loses cash flows and uses up entirely its cash reserve, once funding through debt and equity becomes limited.

One benefit of the Merton model is that it looks forward. Another is that asset value captures the present value of the entire stream of future free cash flows. Hence, a single cash flow can make the firm fail, and cumulated cash drains cannot as long as the firm has sufficient upside potential. This is exactly what happens when high growth firms keep having negative profit, and remain cash-eating machines for a while until they finally reach the stage where cash flows become positive, if they succeed in their high expansion phase.

The KMV implementation has several limitations due to the necessity of making it instrumental. For example, default occurs at a given horizon, where the asset value is above or below the debt value. Real situations are more complex than considering debt as a bullet bond with exercise at some horizon. There is no such thing as a simple bullet debt amortized only once with a certain value. In fact, both the asset value and the debt value, linked to interest rates and default risk, follow a stochastic process. In addition, the value of debt, in the KMV model, is a combination of short-term debt and a fraction of long-term debt. This is only a proxy of the actual time structure of debt repayments. Therefore, the simple model falls short of the reality, although the concepts are robust. Moreover, the time path of asset value crosses the default point before the horizon. Therefore, default could occur before the horizon. Modelling such a probability that the asset value hits the default point at any time between now and the horizon requires simulating all time paths. This would add complexity since the default point (debt) also changes with time. Finally, the KMV model ignores such contractual clauses as cross-default on all debts.

Beyond Mertons model, variations exist trying to extend the original framework to new variables. Black and Cox (1976) model default as the asset value going under a preset boundary value. Longstaff and Schwartz (1995) model default with the same rule, but the risk-free rate is stochastic and follows the one-factor Vasicek model. In addition, they include a correlation between the interest rate and the asset value processes. This allows us to explore what happens to credit spreads when the firm gets closer to default. Other models have introduced various variations. For instance, the boundary value triggering default could relate to the market value of debt. In fact, this would make the valuation of assets comparable to debt, when combined with interest rate volatility. Others consider the influence of the cost of bankruptcy and taxes in the trade-off of borrowers considering exercising their default option.