# Wolfgang Hafner and Heinz Zimmermann, eds.: Vinzenz Bronzin's Option Pricing Models: Exposition and Appraisal.

Wolfgang Hafner and Heinz Zimmermann, eds. Vinzenz Bronzin's Option Pricing Models: Exposition and Appraisal. Berlin and Heidelberg: Springer-Verlag. 2009. Pp. 562. ISBN 978-3-540-85710-5. EUR 159.95 (net), EUR 171.15 (recommended); US$219.00; CHF 248.50; 144.00 [pounds sterling].When Heinz Zimmermann and Wolfgang Hafner (2007) announced their discovery of Vinzenz Bronzin's 1908 monograph Theorie der Pramiengeschafte (Theory of Premium Contracts), they entitled their journal article 'Amazing discovery: Vincenz Bronzin's option pricing models'. They were right: Bronzin's long-forgotten 85-page study, published in Leipzig and Vienna by a Trieste professor of political and commercial arithmetic eight years after Louis Bachelier's once neglected but now famous Theorie de la speculation (1900), is a remarkable mathematical analysis of option pricing, deriving formulas similar to the option pricing formula of Fischer Black, Robert C. Merton, and Myron Scholes in the early 1970s (for which Merton and Scholes shared the Nobel Prize). Like Bachelier, Bronzin based his analysis on the fundamental principle that option prices (and asset prices more generally) would offer speculators an expected profit of zero. As Hafner and Zimmermann (p. 2) acknowledge, 'From a probabilistic standpoint, the work is no match for Bachelier's stochastic foundations, but from a practical and applied perspective, it is full of important insights, results, and applications'. The variation in the titles of Vincenz or Vinzenz or Vincenzo Bronzin's given name is also appropriate, as a reflection of the complicated history of Trieste in Bronzin's lifetime. In the present volume, Hafner (a free-lance researcher and financial historian in Switzerland) and Zimmermann (a finance professor at the University of Basel) provide a facsimile reprint of Bronzin's original German text, an annotated English translation, and essays on Bronzin's contribution and context presented at the centenary conference in Trieste in 2008. Apart from the lack of an index (despite the high price), this valuable volume will be the definitive reference on an intriguing, previously unknown contributor to mathematical finance. Occasionally, the editors overreach a bit, hailing prewar Trieste as 'a true melting-pot of people from different nations' (p. 2) because James Joyce lived there, and reporting that 'the work of Louis Bachelier was well known in Italy shortly after being published' (p. 247, n. 64) because one economist, Alfonso De Pietri-Tonelli, referred to him. In general, however, the editors offer conclusions solidly based on evidence and extensive knowledge of the relevant literature. They have made an 'amazing discovery', and provide context for it with papers on the financial world and cultural landscape of Trieste, actuarial science in Trieste, the journal that published the sole review of Bronzin, and, in several papers, the history of options markets and hedging (including 'A Short History of Derivative Security Markets' by Ernst Juerg Weber of the University of Western Australia). Inevitably, the conference papers vary in quality and interest (and a photograph caption on page 12 describes Bronzin as 'circumvented by alumnies' [sic] at his retirement celebration), but overall the volume is a fascinating and valuable presentation of unfamiliar material.

Born in 1872 in Istria as Vincenzo Bronzin in what is now Croatia, Bronzin (by then Vinzenz) studied engineering at Vienna's Polytechnic University and mathematics at the University of Vienna, attending Ludwig Boltzmann's lectures on the kinetic theory of gases. According to an obituary by his nephew, Bronzin was known as a gambler and fencing champion while a student in Vienna. In 1897, he became a high school mathematics teacher in Trieste, then the port of the Austro-Hungarian Empire (which is how land-locked Hungary later had an admiral as dictator). Starting with marine insurance, Trieste was a centre of insurance. Two Trieste-based insurance companies, Assicurazioni Generali, then as now one of the world's biggest insurance companies, and RAS (Riunione Adriatica di Sicurta, part of Allianz Group since 2005), were the two largest enterprises in the Empire. As professor of political and commercial arithmetic at Trieste's Imperial and Royal Academy of Commerce and Navigation from 1900 to 1910, Bronzin taught applied mathematics to future employees of Trieste's insurance companies, banks, and international trading firms, especially actuaries for Generali and RAS. Bronzin's three publications were based on his lectures: a five-page article in 1904 on currency arbitrage in a German periodical for commercial education, an unremarkable 1906 textbook on political arithmetic (applying basic mathematics to compounding, annuities, and life expectancy tables), and, although options were not traded on the small Trieste bourse, his extraordinary 1908 monograph on option pricing. From 1910 to his retirement in 1937, Bronzin was director of the Trieste academy and, after World War I, its Italian successor (resuming the given name Vincenzo). He lived in Trieste until his death in 1970 at the age of 98. Although described in a 1925 book about the Trieste academy as 'a jewel of humanity' and 'heroic scientist' (quoted by Hafner and Zimmermann 2009, p. 8), Bronzin published no further research after becoming an administrator. In contrast, Bachelier attempted repeatedly over four decades to secure an audience for his theory of speculation, without success.

Like Bachelier (1900), Bronzin (1908) mentioned no other author. Whether Bronzin knew Bachelier (1900), like the question whether Bachelier knew Jules Regnault (1863), remains a mystery (on Regnault's non-mathematical exposition of the implications of a zero expected speculator's profit, see Franck Jovanovic in Poitras 2006). Bronzin (1908), like his 1906 textbook on political arithmetic, was published in Leipzig and Vienna by Franz Deuticke, who also published Sigmund Freud and the probability theorist Richard yon Mises, but attracted little attention. The only known review, a mere four sentences, unsigned, in Vienna's Monatshefte fur Mathematik und Physik in 1910, concluded that 'It is unlikely that the respective results will ever be of notable practical value, as the author himself seems to imply' (p. 335)--and Hafner (p. 355) thinks it was Bronzin's former teacher Gustav von Escherich (the journal's editor) who delivered that crushing dismissal. Another unsigned review in the same issue disdained as 'certainly not very plausible' the analysis of de Montessus (1908), a book by Bachelier's Paris colleague who included a chapter on 'Bachelier's Theorem' that the mathematical expectation of the speculator is zero. However, in 1913 the same journal carried a positive review of Bachelier (1912), probably by Ernst Blaschke (Hafner in Hafner and Zimmermann 2009, pp. 355-56). In the subsequent literature, the option pricing model of Bronzin (1908) was developed further in only one article, by Gustav Flusser (1910-11) in the yearbook of the Prague commercial academy where Flusser taught, and received only a passing mention in a footnote in Friedrich Leitner's banking textbook in 1920 that Bronzin dealt with derivatives contracts from a mathematical standpoint (Hafner and Zimmermann 2009, pp. 18-19, 332).

So, Bronzin's striking work on option pricing was known, if at all, only to people in Trieste engaged in actuarial science and insurance economics at a high mathematical level--a more interesting potential audience than one might suppose, because it included Bruno de Finetti, the eminent mathematician, actuarial scientist, and pioneer of subjective probability. As Flavio Pressacco recounts in his chapter on 'Bruno de Finetti, Actuarial Sciences and the Theory of Finance in the 20th Century', de Finetti, born in Innsbruck, spent his childhood in Trieste and returned in 1931 to work for Generali, spending many years in Trieste as head of Generali's research department (see also Gillies and Ieto-Gillies 1987, not cited by Pressacco). De Finetti (1940), on the mean variance approach to financial decisions under uncertainty, on expected utility, and on risk aversion, has recently been translated. In an article entitled 'De Finettit Scoops Markowitz', Nobel laureate Harry Markowitz (2006) acknowledges de Finetti's priority in using mean variance analysis and credits de Finetti with solving a special case of the global optimality conditions in quadratic programming. Although Pressacco's chapter does not even mention Bronzin, readers will be as curious about possible contact between de Finetti and Bronzin in Trieste as one is about Bronzin's possible knowledge of Bachelier (1900) or about Bachelier's possible knowledge of Regnault (1863).

Hafner, Zimmermann, and their contributors tell a fascinating story, one that few if any readers will already know. Bronzin's remarkable 1908 analysis of option pricing, which looks so modern in retrospect, was (unless de Finetti knew Bronzin's work) even more isolated than Bachelier (1900), which at least influenced de Montessus (1908) and Alfred Barriol, and was followed by four decades of further publications by Bachelier on probability such as Bachelier (1912), which influenced Andrei Kolmogorov. The editors are to be commended for the definitive reference on Bronzin, and the publisher reproved for not giving this very expensive reference work an index.

References

Bachelier, Louis. 1900. Theorie de la speculation. Paris: Gauthier-Villars; translated in Cootner (1964) and Davis and Etheridge (2006).

Bachelier, Louis. 1912. Calcul des probabilites, Tome I. Paris: Gauthier-Villars.

Cootner, Paul, ed. 1964. The Random Character of Stock Market Prices. Cambridge, MA: MIT Press.

Davis, Mark, and Etheridge, Alison. 2006. Louis Bachelier's Theory of Speculation. Princeton, N J: Princeton University Press.

de Finetti, Bruno. 1940. 'II problema dei pieni', Giornale Instituto Italiano Attuari, 11, 1-88, trans. L. Barone (2006) as 'The problem of full risk insurance, Chapter 1: The problem in a single accounting period', Journal of Investment Management 4, pp. 19-43.

Flusser, Gustav. 1910-11. 'Uber die Pramiengrosse bein den Pramien- und Stellagegeschaften', Jahresbericht der Prayer Handelsakademie.

Gillies, D. A. and Ietto-Gillies, G. 1987. 'Probability and economics in the works of Bruno de Finetti', Economia Internazionale 40, pp. 192-209.

Markowitz, Harry. 2006. 'De Finetti scoops Markowitz', Journal of Investment Management 4, pp. 5-18.

Montessus de Ballore, Robert, vicomte de. 1908. Lecons elementaires sur le calcul des probabilites. Paris: Gauthier-Villars.

Poitras, Geoffrey, ed. 2006. Pioneers of Financial Economics, Vol. 1: Contributions before Irving Fisher. Cheltenham, UK, and Northampton, MA: Edward Elgar Publishing.

Regnault, Jules. 1863. Calcul des chances et philosophie de la bourse. Paris: Mallet-Bachelier.

Zimmermann, Heinz, and Hafner, Wolfgang. 2007. 'Amazing discovery: Vincenz Bronzin's option pricing models', Journal of Banking and Finance 31, pp. 531-46.

Robert W. Dimand, Department of Economics, Brock University, St. Catharines, Ontario L2S 3A1, Canada. Email: dimand@brocku.ca.

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Author: | Dimand, Robert W. |
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Publication: | History of Economics Review |

Article Type: | Book review |

Date: | Jan 1, 2011 |

Words: | 1666 |

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