Mathematical models are, after all, bricolage constructions inscribed with curdled utopias

For traders to use a model such as Black–Scholes is not like a medieval monarch making someone an outlaw by saying that they are an outlaw: no mathematical fiat.

Options had been traded for centuries, but typically in only an informal, semi-organized way—in the interstices or on the peripheries of mainstream financial markets

[...] our argument—our claim of counterperformativity—is that those assumptions made possible, via their gaming by market participants, the construction of securities that radically undermined them.

In a stimulating contribution to the literature on performativity in economic life, Elena Esposito points to the pervasiveness of what, drawing upon the social theory of Niklas Luhmann, she calls ‘second-order observation’. Translated into our terms, it is not simply that mathematical models in finance have performative and counterperformative effects, but actors observe or anticipate those effects and act accordingly. A recurring suspicion that actors within finance have about the many models that involve the bell-shaped normal distribution, on which extreme events are very unlikely, is that their use can have the counterperformative effect of increasing the likelihood of those events.

He was fond of an autobiographical synecdoche: when interviewed, he said that an important thread running through his work began with a book review he found in his uncle Szolem’s wastepaper basket

[...] Nor do we for a moment intend that investigation of the performativity or counterperformativity of mathematical models should displace other forms of analysis of finance. For instance, the rise of options and other forms of derivatives cannot be understood in isolation from broader processes such as the collapse of the Bretton Woods agreement and the rise of free-market economics and of deregulatory impulses. To take an example of a quite different kind, Chicago’s open-outcry trading pits were places of the body as well as of the use of Black’s sheets—and specifically places of male bodies, places often uncomfortable for women. The patterns of interpersonal relations among options traders left their traces on price movements, and, more generally, the structures of financial markets—including the advantages enjoyed by incumbents—remain important, even in today’s world of algorithmic trading. The causes of the global financial crisis go far beyond the counterperformative process on which we have focused, and centrally include phenomena of the sort focused on by political economy of a more traditional kind, including Marxist political economy. As such, all we would claim is that ‘performativity’ is a useful addition to the conceptual toolkit necessary for understanding economic life. Mathematical models are by no means the only phenomena that have a performative aspect, but they are ever more important. An algorithmic economy is an economy of logical operations and mathematical procedures, and therefore a mathematical economy.