A Review Of "The Pricing of Options and Corporate Liabilities"

This year we celebrate the 50th anniversary of the seminal paper "The Pricing of Options and Corporate Liabilities" in which the famous Black-Scholes formula was introduced. We will chronicle and review the literature predating and postdating the publication of this work in order to identify precisely which new concepts they introduced to the field. Option pricing formulas existed long before Black and Scholes with notable contributions to the field coming from Sprenkle, Rosett, Ayres, Boness, Samuelson, and Merton, amongst others. However, most of these formulas were derived in terms of the historical measure, and each had the goal of estimating the preferences and expectations of investors. As such, they relied on certain non-observable parameters which are very difficult to estimate, and hence introduce a degree of subjectivity to the formulas. Since the risk attitudes of investors were unknown, Boness assumed that traders in speculative markets were risk-indifferent, and considered a probabilist approach to derive his pricing formula. Despite being disregarded in the literature, it happens to be the celebrated Black-Scholes formula. Through making a set of specific assumptions, Black and Scholes deviated from these previous attempts by formulating a PDE which only depends on observable parameters. Therefore, the Black-Scholes formula was significantly simpler than its predecessors, with a single parameter to estimate, making it the market standard. Not only had Boness already derived the same BS-formula, but Samuelson, Merton, Cox and Ross were also able to show that the Black-Scholes formula was in fact a special case of its predecessors, obtained by removing references to the mean expected stock price and the investors preferences. That is, by assuming that traders in speculative markets were risk-indifferent. While the Black-Scholes formula relies only on market observables, we will show that it is limited in the sense that we can not use it to estimate certain investor's expectations and preferences. However, it is now well known that risk premia is essential in explaining the dynamics of option prices. Hence, practitioners should price options in the historical measure and explicitly model the investor's expectations and preferences.