Skip to content →

Review of “The Legacy of Fischer Black” edited by Bruce N. Lehmann. (Financial Analysts Journal)

The Legacy of Fischer Black. Edited by  Bruce N. Lehmann. Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016, USA. 306 pages, $65.50.

Reviewed by Emanuel Derman.



In late 1996 I attended a memorial conference organized by the Berkeley Program in Finance in honor of Fischer Black, who had died about a year earlier. Many of the talks delivered there have now been published in this book, accompanied by a thoughtful introduction and an essay by Bruce Lehmann on Black’s approach to valuation.


As Lehmann points out, Black’s main focus  throughout his life was the “determination of the price of risky assets in real-world capital markets.” Black was always driven by the idea of equilibrium, the notion, imported from physics and chemistry, that market prices of assets settle at the values where they provide equal return per unit of risk. Shortly before he died, he once emailed me in response to a question: “I view all our work on fixed-income models as resulting from the application of the capital asset pricing model to fixed-income markets.”


Working within his chosen framework, Black was led not only to the famous options valuation  formula, but also to his contributions to corporate finance, the capital asset pricing model, models of the yield curve, strategies for asset allocation, methods for electronic trading, international asset pricing, and viewing interest rates themselves as options. These were just a few of his interests, many of which are discussed in this book in a variety of broad-ranging papers by renowned financial economists.


What comes through most intensely from the comments about Black in this book is his character. Throughout the years I knew him at Goldman, Sachs & Co., I noticed that you couldn’t easily predict his attitude to one situation by knowing his opinion about another. Yet, his character was a coherent whole even though its parts seem uncorrelated. He simply liked to think through everything for himself.


This characteristic is evident in the quotes from Black scattered throughout the book, all of which illustrate his iconoclastic and independent style of thinking.  Here are a few:


“It’s better to ‘estimate’ a model than to test it. I  take ‘calibration’ to be a form of estimation, so I’m sympathetic with it, so long as we don’t take seriously the structure of a model we calibrate. Best of all, though, is to ‘explore’ a model.”


“My job, I believe, is to persuade others that my conclusions are sound. I will use an array of devices to do this: theory, stylized facts, time-series data, surveys, appeals to introspection and so on.”


“In the real world of research, conventional tests of [statistical] significance seem almost worthless.”


What distinguishes these statements from those of many other academics is Black’s determination to understand both theory and practice, his pragmatic devotion to comprehending reality (I particularly admire his appeals to introspection), and his emphasis on the benefits of rational thinking. In this latter regard, Lehmann reminisces about something I often heard Black say myself: “I recall Fischer saying that managers should be paid in accord with the quality of their reasoning regarding the strategies they employed and not for their ex post performance.”


Black was an unsentimental realist, unafraid to see and take the world for what it is. He applied the same standards to  himself. Once, when I asked him about the appropriate way to refer to the options model – should I call it “Black-Scholes” or “Black-Scholes-Merton?” – he left me voicemail saying was OK to call it the Black-Scholes-Merton model, because it was Merton who had come up with the replication argument for valuing an option. Then he added, quite calmly, that “that’s the part that many people think is the most important.” He said this despite his love of his original equilibrium-based derivation of the Black-Scholes equation.


In the same spirit, several months before his death, Black submitted his final paper to this journal, writing to the editor in the accompanying letter: “I would like to publish this, though I may not be around to make any changes the referee may sug­gest. If I’m not, and if it seems roughly acceptable, could you publish it as is with a note explaining the circumstances?”

This is a broad-ranging well-edited book that provides a good taste of Black’s approach to quantitative finance. I particularly enjoyed Lehmann’s essay on Black’s work, Myers’ discussion of his contributions to corporate finance, and Duffie’s review of the Black-Scholes-Merton approach.

Published in Finance writing