Finding the highest-yielding combination of debts that could achieve the desired ratings was tantamount to finding the riskiest combination. Not only was it always necessary for traders to input a value for volatility before the model could generate a price, but also, for example, the specifications of most of the contracts traded on the new options exchanges differed from those in the model’s canonical solution. Roubaud was content to look to mathematics for inspiration: for the axioms and structures through which to generate his ‘potential literature’. Indeed, Le Lionnais hinted at this discursive unification project in his commentary: ‘Bourbaki’s message, so rich and so dense with meaning, has as its overall aim a systematic inventory of the analogies in mathematics and at the same time an elucidation of their validity and of their significance’.footnote17. Silas Van Boi Laithang. The third mechanism of counterperformativity is what we call ‘deliberate counterperformativity’: the use of a model with the conscious goal of creating a world radically at odds with the world postulated by the model. We’ve heard two thirds of them Are false, or worse, are nonsense. ‘We must’, Weil said, ‘write a treatise that could be used by anyone: by researchers (university lecturers or not), by students, by future educators, by physicists and by all engineers’.footnote8 As such, the tools of mathematics were to be given in the most universal form. The manifesto challenges its reader with absurd, overblown questions: ‘Do you remember the polemic that accompanied the invention of language?’; ‘And the creation of writing, and grammar, do you think that happened without a fight?’; ‘Should humanity lie back and be satisfied to watch new thoughts make ancient verses?’footnote29. It was therefore a considerable surprise to MacKenzie when in fieldwork in Chicago in 1999–2000 he found those distributions being used by the Options Clearing Corporation (occ). The case of this on which we focus involves a family of mathematical models advocated by the maverick French mathematician, Benoit Mandelbrot, who stood opposed both to mainstream financial economics (such as the Black–Scholes model) and to the form of ‘modernist’ reasoning hegemonic in mid-twentieth century mathematics.footnote9 As we will see, the family of models in question was adopted precisely to reduce the chances of the world they posited becoming real. The analogy between literature and mathematics is essential to the Oulipo. After the day’s trading on 19 October, staff of the Mercantile Exchange’s clearinghouse stayed up all night, desperately trying to achieve the transfers of funds necessary to balance the clearinghouse’s books and allow the Exchange to open on 20 October, a process that was completed, with only three minutes to spare, by what was in effect an emergency loan from the Continental Illinois Bank, verbally agreed in a phone call with the bank’s chair.footnote35 The firms of ‘specialists’ that kept trading going on the New York Stock Exchange exhausted much of their limited capital on 19 October, and its chair John Phelan kept it formally open on 20 October—even though, in the absence of buyers, trading in most stocks had ceased—only because he had received an appeal from the White House not to close, and privately feared that any closure would be permanent.footnote36, The trauma seems to have had enduring, possibly permanent, effects on the pricing of options. The final part of the article—our conclusion—briefly considers the place of performativity and counterperformativity in the analysis of finance. The first effect of the model on which we will focus is the most clear-cut: its effect on how professional options traders talked about options. She was a scrupulous copy editor, happy to muck in with office life or plan after-work sorties; taking part in all the everyday discussions about texts and things. Indeed, options traders soon came to talk about what they were doing as buying or selling volatility, not just buying or selling options. The ‘axiomatic method’ is Bourbaki’s insurance against the threat of the discipline’s fragmentation: against the possibility of mathematics becoming ‘a tower of Babel of autonomous disciplines’. Optimistic speculators might, for instance, be anticipating that the shares were going to rise in value, but simply buying those shares outright would be expensive. The lower the value of alpha, the more fat-tailed the distribution. Bourbaki’s thunderbolt, the Éléments de mathématique, began its life as a somewhat modest, conventional project. James R Ferris. Formal experimentalism was equally evident in their historiographic method. Does it have the slightest chance to take root in the cultural tissue of a society and to produce leaf, flower, and fruit? The deployment of mathematics as an organizing metaphor and appeals to the epistemic virtues of mathematics are, indeed, common strategies in the construction of literary and artistic movements: Novalis’s definition of Romanticism, T. E. Hulme’s geometrical classicism, or the mathematical analogies of Pound’s vorticist manifestos, for example. Rather, 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. If they did this, then they would enjoy a pattern of returns similar to those that would result from buying a put, without incurring the full expense of the latter. ‘Potential Literature’ is announced as imminent, necessary and urgent: witness ‘the impatience of the starving multitudes’. Kyle John Stuart. Tori Jay Phyllis Livermore . We have no illusion that our three-fold categorization of counterperformativity is complete: we expect that others can add to it, and hope that they will do. An investor in those shares could, for example, purchase a put option that gives her the right to sell them at $30. Mandelbrot was briefly a major influence on the University of Chicago economists developing the efficient-market view of finance, especially on the formulator of the most explicit form of the efficient-market hypothesis, Eugene Fama.footnote48 An infinite variance, however, renders standard econometric procedures inapplicable, and, after mainstream financial economics’s short-lived flirtation with Lévy distributions, it turned its back on them. Hence counterperformativity. Indeed, as the manifesto is a genre of potentiality—positioned between what has been done and what is to be done—it is a particularly suitable vehicle for the group’s ‘Potential Literature’. 3 May 1882, d. 27 Dec 1977; George Douglas … … And likewise game theory, until von Neumann.footnote27, Oulipo draw on mathematics—combinatorial techniques, Boolean algebra and Bourbaki’s axiomatic method, for example—in their literary practice. Her next, ‘Intaglio as Philosophy’, found Bachelard labouring in the same trench as Bouvard and Pécuchet. Their underlying model of share-price movements was also standard: they assumed that those movements followed a ‘random walk’ in which price changes in successive time periods were independent of each other. In ‘The Foundations of Literature (after David Hilbert)’, Queneau formulates an axiomatic system for literature.footnote37 The text is at once a tribute to Hilbert, a pastiche of Hilbert’s axiomatic style and a critique of Hilbert. As Judith Butler notes, ‘financial theories . 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. In Le Lionnais’s re-casting, the Quarrel of the Ancients and the Moderns functions as a grandiose prehistory for the advent of Oulipo. Bourbaki, however, were not concerned with ‘languages’ in the plural. Bourbaki’s published writings and their archives show the tangled visions and discordant notes of their utopianism. 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 . … Black and Scholes, for example, had difficulty persuading the Journal of Political Economy to publish the paper that eventually led Scholes (and Merton) to Stockholm and the 1997 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel: understandably, given the marginality of options to the financial system at the start of the 1970s, the journal’s editor regarded their paper as of only limited interest.footnote20 Nor did traders have any automatic faith in the correctness of the Black–Scholes model. ), Furthermore, disentangling causality is made difficult by the fact that the publication and first uses in trading of the model coincided in time almost exactly with the opening of the cboe, at which point options changed from being simply ad hoc contracts sold by brokers (often to members of the general public), and became standardized contracts on an organized exchange on which professional traders could compete both to buy and to sell options. . . In late 2016 she applied for an internship at Verso, where she pulled together ideas for a philosophy of science list—scouting, she laughingly put it, for the next Paul Feyerabend. 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, and often in quiet violation of legal bans on options trading: options were often felt to be little better than wagers. that the calculation of probabilities was at first nothing other than an anthology of ‘diversions’, as Bourbaki states in the ‘Notice Historique’ of the twenty-first fascicle on Integration. Alice, who set up a hip-hop record label called Emancipated, lives on an 11-acre California estate, One Gun Ranch, with Ann Eysenring, estate agent to the stars. If the occ were to fail—like the clearinghouse of the Chicago Mercantile Exchange, occ was also in peril in the aftermath of the 1987 crash, with staff spending three successive nights awake in their offices, and with the Federal Reserve having to intervene to avert the bankruptcy of the occ’s leading member firm, First Options—then organized options trading in the United States would collapse.footnote49. That can indeed be viewed as a form of insurance, limiting the losses that the investor will suffer if the shares plummet in price. It mocks the preface-manifesto, the ‘directions for use’, of Bourbaki’s Éléments. Henri Cartan and André Weil were two young mathematicians responsible for teaching courses on differential and integral calculus at Strasbourg. Bourbaki describe their ‘axiomatic method’ as a way to transcend the limitations of specialization. The arts of reading and of writing mathematics require a kind of double vision: ‘Thus, written in accordance with the axiomatic method and keeping always in view, as it were on the horizon, the possibility of a complete formalization, our series lays claim to perfect rigour.’ Bourbaki’s mathematical structuralism sounds rather like linguistic structuralism here (they could be discussing the langue and parole of mathematical language), and indeed they reference linguistics in defence of their project: Just as the art of speaking a language correctly precedes the invention of grammar, so the axiomatic method had been practised long before the invention of formalized languages; but its conscious practice can rest only on the knowledge of the general principles governing such languages and their relationship with current mathematical texts.footnote21. We have some sympathy with another set of critics of the application of the latter to economic life, of which Philip Mirowski is the most prominent.footnote52 An analysis that neglected Derrida’s and Butler’s warnings, and focused only on cases of ‘successful’ performativity, might promote a renewed form of complacency, in which mathematical models—or, for example, other forms of orthodox economics—are indeed seen as ‘working’ (albeit not because they begin as correct representations of the world, but because they have the power to change it). The whole story vanishes, the successive tentative formulations of the theorem in the course of the proof-procedure are doomed to oblivion while the end result is exalted into sacred infallibility’. . Although in recent years there has been a growing critical interest in the intersection of literature and mathematics and in the Click here to find personal data about Caroline Bamford including phone numbers, addresses, directorships, electoral roll information, related property prices and other useful information. The minutes of this meeting record: weil presents his project—to establish the content of the certificate in differential and integral calculus for the next 25 years by jointly writing a treatise on analysis. The 1919 Birthday Honours were appointments by King George V to various orders and honours to reward and highlight good works by citizens of the British Empire. alice bamford new left review. Why ‘counterperformativity’, and not simply ‘performativity’? Nonetheless, Bourbaki’s nonformal structuralist image of mathematics gained traction both inside and outside the discipline of mathematics—evident not least in the formation of Oulipo itself. The feature of patterns of options prices that seems most likely to be related to the use of the Black–Scholes model concerns the crucial input to the model, volatility. Mandelbrot claims he spent only one day as a student of the École Normale Supérieure in 1945: resigning after the first day because he saw that the ‘Bourbaki cult’ was taking over the school.footnote43 He wrote in his memoirs that his uncle, the Bourbaki member Szolem Mandelbrojt, was ‘upset and afraid’ by his nephew’s decision to change schools: ‘the way any fanatic, scientific purist fears new alloys’.footnote44. ‘Gamma’ is the second derivative, the rate at which delta changes—and thus the rate at which the hedge needs to change—as the price of the underlying asset moves. . There are, certainly, broad parallels between ‘modernist mathematics’ and other forms of cultural modernism: a rupture with tradition, a turn toward formalism, and a heightened self-reflexivity. “It’s about making the best-informed choices,” she says. Once again, the difficulties of establishing historical causation intervene: it is hard to be certain, even in retrospect, just how much portfolio insurance contributed to the crash.footnote34 What cannot be gainsaid, however, is the extent to which the events of that terrible Monday sparked fears of the collapse of the us financial system. Bibliographical references are gathered together in Historical Notes, usually at the end of each chapter. Queneau thus stages a confrontation between the axiomatic method and the particularities of literature, creating a manifesto that enacts, via its own internal logic, the impossibility of complete formalization.footnote38. There are uncomfortable analogies to the current epoch: a right-wing President, tax cuts, a big expansion in government debt, an economic boom, and a stock-market surge accompanied by growing fears over its durability. Bamford was, after all, raised on a farm—her family owns and operates the organic behemoth Daylesford in the Cotswolds, which Alice lovingly calls the mothership. That made thinking and talking about options vastly easier: the dozens or hundreds of options on a given stock could all be compared on the single numerical dimension of implied volatility. . Banking regulators also in effect outsourced some of their tasks to rating agencies, whose grades were an important input into the determination of necessary levels of equity. In the highly mathematical world of modern finance, even the phrase traders use to identify the danger is mathematicized. My research is on the sociology of markets, focussing on automated trading and online advertising. That no one has ever succeeded in doing this doesn’t prove a priori that it’s impossible . When faced with ‘complex mathematical objects’, Bourbaki ‘separate their properties’—algebraic properties, topological properties, and so on—and ‘regroup them around a small number of concepts’: they ‘classify them according to the structures to which they belong’. . Because, so to speak, a normal distribution does not ‘expect’ an extreme price movement, if one occurs, the statistical estimator of the key parameter, the variance of the distribution, can suddenly soar. There can be dozens or even hundreds of different options contracts on a single stock: the call options explained above; put options (described in the next section); different ‘strike prices’ (the ‘strike price’ of a call, for example, is the price at which the call’s holder has the right to buy the underlying shares); different expiry dates; etc. I've worked in the past on topics ranging from the sociology of nuclear weapons to the meaning of proof in the context of computer systems critical to safety or security. ‘Counterperformativity’, however, is more than a routine misfire. The group met on 10 December 1934 to discuss this ‘Traité d’Analyse’. Click here to find personal data about Alice Bamford including phone numbers, addresses, directorships, electoral roll information, related property prices and other useful information. Mathew Gladstein, of the investment bank Donaldson, Lufkin & Jenrette, was one of the first traders (perhaps the first trader) to use their model: he had contracted with Scholes and Merton to provide him with theoretical options prices ready for the opening of the Chicago Board Options Exchange (discussed in more detail below) on 26 April 1973. do not function as sovereign powers or as authoritative actors who make things happen by saying them’.footnote12 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. Leah Maree Hammond. We would like to show you a description here but the site won’t allow us. It is not a danger restricted to put options or to the Black–Scholes model alone. Although the ratings profiles of mbss, abss and cdos remained broadly stable through time, the quality of the debts that made them up deteriorated. That a mathematical model of option prices should have had any major effects at all is, in one sense, quite surprising, since the question of how options should be priced had long seemed an intriguing but essentially minor issue. Donald MacKenzie, Alice Bamford: Counterperformativity https:// newleftreview.org / II/ 113/ donald-mackenzie-alice-b amford-counterperformativity. Sue was born on November 22, 1943 in Montreal, Quebec. Lakatos’s stated enemy was the ‘formalist’ philosophy of mathematics. MyHeritage Family Trees; Geni World Family Tree; England & Wales, Death Index, 1837-2005; BillionGraves; FamilySearch Family Tree ; 1921 Canada Census; 1881 England & Wales Census; 1901 England … ‘Equity’ is thus the crucial risk-absorbing cushion. When one trader or one algorithm sells an option, and another trader or algorithm buys that option, they do not enter into a contract with each other: each of them enters into a contract with the occ.