On a late summer’s evening in 1956, the bbc’s Third Programme broadcast—in two 45-minute parts, separated by a gramophone recording of Ravel’s song cycle, Histoires naturelles—a talk on ‘Performative Utterances’ by J. L. Austin, Professor of Moral Philosophy at the University of Oxford. The term ‘performative’ (which he admitted was ‘ugly’, even though it seems to have been he who coined it) signalled a crucial shortcoming in the positivist prejudice that ‘the sole interesting business . . . of any utterance is to be true or . . . false’. As Austin told his listeners, there are perfectly meaningful statements in ordinary language that are neither true nor false, utterances in which the speaker ‘is doing something’ rather than asserting something about a state of affairs external to the utterance—performative utterances. Imagine, for instance:

that in the course of a marriage ceremony I say, as people will, ‘I do’—( . . . take this woman to be my lawful wedded wife) . . . [W]hen I say ‘I do’ . . . I am not reporting on a marriage, I am indulging in it.footnote¹

Austin’s attention to the performative has survived the eclipse of the Oxford ‘ordinary language philosophy’, of which he was a leader. Especially via Jacques Derrida—with his famous critique of the Austinian assumption of ‘the conscious presence of the intention of the speaking subject in the totality of his speech act’footnote²—and Judith Butler’s hugely influential theorization of gender, the idea of ‘performativity’ has become a pervasive reference point in the humanities and social sciences.

‘Performativity’ has, for example, been employed by the French economic sociologist Michel Callon as a way of denoting the capacity of a mathematical model or other aspect of ‘economics’ (a term he understands in a very broad sense, far broader than just the academic discipline) to be more than a representation of some external reality.footnote³ A model can do things, just as an utterance in everyday speech can (albeit in quite a different way). Performativity is, for instance, a particularly pertinent issue for mathematical models in finance. When such a model escapes from the lecture theatres and pages of academic journals into the wild—when it starts being used by financial practitioners, regulators and so on—it can affect the very phenomena it purports to describe.

Our argument is this: when analysing the effects of mathematical models on financial markets, attention ought to be paid not just to performativity, but also to ‘counterperformativity’.footnote⁴ Austin himself, and many of those who have drawn on his work (such as Pierre Bourdieu), have been sharply aware that, as Austin put it, more is involved in performativity than ‘the uttering of the words of the so-called performative’. (In the case of ‘I do’, for example, both partners must legally be free to marry, the ceremony must be conducted according to certain rules and by an authorized person, etc.) What Austin called ‘misfires’ or ‘infelicities’—‘the things that can be and go wrong on the occasion of [intended performative] utterances’—are commonplace.footnote⁵ Indeed, for Derrida and Butler, apparent failure is intrinsic to performativity’s productivity: ‘a successful performative is necessarily an “impure” performative’; ‘rupture or failure . . . characterizes every interstitial moment within iteration’; ‘breakdown [is] constitutive to the performative operation of producing naturalized effects’.footnote⁶

What, then, is our neologism good for? How can we, a sociologist (MacKenzie) and a literary theorist (Bamford), use counterperformativity to analyse the operations of finance and the epistemology of mathematical modelling? Abstraction and empiricism are intertwined in the very notion of counterperformativity, making it a particularly useful concept for our analysis of the curious ways in which models ‘fail’. Mathematical models are, after all, bricolage constructions inscribed with curdled utopias, with arms and with rights—so many scraps of social history.footnote⁷ Misfires are all-pervasive in the application of mathematics to finance: markets seldom if ever behave exactly as posited by even the most sophisticated model. ‘Counterperformativity’, however, is more than a routine misfire. It is more than just what Michel Callon—as noted above, the pioneer of the application of ‘performativity’ to economic life—calls, in translating ‘counterperformativity’ into his terminology, the failure of agencements (loosely, arrangements of human beings and non-human entities that generate specific forms of agency) ‘to discipline and frame the entities that they assemble’.footnote⁸ Counterperformativity is a very particular form of misfire, of unsuccessful framing, when the use of a mathematical model does not simply fail to produce a reality (e.g. market results) that is consistent with the model, but actively undermines the postulates of the model. The use of a model, in other words, can itself create phenomena at odds with the model.

This article proceeds as follows. First, to anchor the discussion, we consider the context and effects of what is arguably the twentieth century’s most influential mathematical model in finance, the Black–Scholes model of options, which was hugely important to the emergence from the 1970s onwards of giant-scale markets in financial derivatives. (A ‘derivative’ is a financial instrument whose value depends upon the price or level of another ‘underlying’ instrument, such as a block of shares. We explain ‘options’, which are a type of derivative, below.) Then we take on the article’s main task, which is to sketch the beginnings of a typology of forms of the counterperformativity of mathematical models in finance.