Amazing Discovery : Professor Bronzin's Option Pricing Models (1908)

The doctoral thesis of Louis Bachelier (1900) is widely considered as the seminal work inoption pricing theory. However, only a few years later, 1908, Vinzenz Bronzin, who wasa professor of actuarial science at the Accademia di Commercio e Nautica in Trieste,published a booklet (in German) on option pricing as well. While his approach is morepragmatic than Bachelier’s, every element of modern option pricing can be found: Riskneutral pricing, no-arbitrage and perfect-hedging pricing conditions, the put-call-parity,and the impact of different distributional assumptions on option values. In particular, heshows how the normal law of error – which is the normal density function – can be usedto price options, and how it is related to a binomial stock price distribution. His equation(43) is closer to the Black-Scholes formula than anything published before Black, Scholes,and Merton. He moreover develops a simplified procedure to find analytical solutionsfor option prices by exploiting a key relationship between their derivatives (with respectto their exercise prices) and the underlying pricing density. Besides of pricing simplecalls and puts, he develops formula for chooser options and, more important, repeatoptions.While the book got some attention in the academic literature in the time when it was published(including a not very supportive book review as well), it seems to have been forgottenlater. We have just found one modern reference to the book (which is independentof our own research), which is easily verified by a Google search request. It is thepurpose of this paper to present the major results of the book, and to highlight its contributionin the light of modern option pricing theory.Our “discovery” also raises questions beyond the analytics: why did the results of Bachelier,Bronzin, and possibly other’s yet to be re-discovered, not get a broader acceptance?Why did their research not find immediate successors, academics that made it a subjectof ongoing scientific research? Finding answers to these questions c