One way to think of the value of a risky firm is through expected measure theory. On the most basic level, the value of any asset is the convolution of the probability density function of its risky payoffs onto the outcome space of these risky payoffs. In this view, equity is analogous to perpetual long call option on the value of a firm, while debt is seen as a short put option on its value.
However, practitioners have not broadly adopted the use of options theory in pricing underlying corporate assets and liabilities. Real options analysis has found some acceptance among specialists', but the inputs and theory to these analyses are subjective and applications are not consistent. Why has this original use of the rational pricing of risky cash flows failed to become more broadly adopted?
In Samuelson & McKean (1965), McKean derived a closed-form solution for pricing perpetual options. The use case of such an approach was intended to value warrants, but was also intended for use in pricing more general corporate assets and liabilities.
In Merton (1973), "the possibilities for further extension of the theory [of rational option pricing] to the pricing of corporate liabilities are discussed".
In Black-Scholes (1973), the authors devote an entire section of the paper to discussing the applicability of rational pricing to corporate stocks and bonds:
It is generally not realized that corporate liabilities other than warrants may be viewed as options. Consider, for example, a company that has common stock and bonds outstanding and whose only asset is shares of common stock of a second company... Under the conditions, it is clear that the stockholders have the equivalent of an option on their company's assets. In effect, the bond holders own the company's assets, but they have given options to the stockholders to buy the assets back. The value of the stock at the end of 10 years will be the value of the company's assets minus the face value of the bonds, or zero, whichever is greater.
In Cox-Ross (1976), the authors use discrete models to "find explicit option valuation formulas, and solutions to some previously unsolved problems involving the pricing of securities with payouts and potential bankruptcy."
In Geske (1978), the author:
...presents a theory for pricing options on options, or compound options. The method can be generalized to value many corporate liabilities. The compound call option formula derived herein considers a call option on stock which is itself an option on the assets of the firm. This perspective incorporates leverage effects into option pricing and consequently the variance of the rate of return on the stock is not constant as Black&Sholes assumed, but is instead a function of the level of the stock price. The Black&Sholes formula is shown to be a special case of the compound option formula. This new model for puts and calls corrects some important biases of the Black-Scholes model.
The list of academic support continues almost indefinitely, but I still very rarely see it applied.
With some much theoretical and anecdotal support, I am surprised that this topic hasn't found broader support. I can surmise a few reasons why it is not broadly used. Chief among these, markets for underlying assets are not complete, and arbitrage relationship between risky cash flows and their underlying drivers can be very firm-specific (or even totally ambiguous). There may be other reasons, but I wanted to gather some input from the community on your opinions. Maybe the theory is more broadly used than I realize, in which case, I'd also like to know where and how.
