Esposito's temporality of finance: Endogeneity and revisability in derivative transactions

Husbands, Conor Article Esposito's temporality of finance: Endogeneity and revisability in derivative transactions Finance and Society Provided in Cooperation with: Finance and Society Network (FSN) Suggested Citation: Husbands, Conor (2020) : Esposito's temporality of finance: Endogeneity and revisability in derivative transactions, Finance and Society, ISSN 2059-5999, University of Edinburgh, Edinburgh, Vol. 6, Iss. 2, pp. 114-129, https://doi.org/10.2218/finsoc.v6i2.5270 This Version is available at: https://hdl.handle.net/10419/309385 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Email: sedm3[email protected]. https://doi.org/10.2218/finsoc.v6i2.5270 Conor Husbands Independent scholar, UK Abstract Recent years have seen greater interest in the theoretical foundations of abstract finance and their intersection with questions of philosophy and sociology. In particular, exchanges between authors such as Donald MacKenzie, Timothy Johnson, Elie Ayache, and others have debated the deterministic or contingent dynamics of markets, as well as their interdependency with the theories that purport to describe them. Working in this tradition, Elena Esposito raises a novel question in her 2011 book, The Future of Futures: could the exchange of derivative securities within financial markets entail not so much the provision of liquidity, but the transaction of time? In this article, I reconstruct Esposito’s analysis, arguing that the proper response to this question should be affirmative. Particular emphasis is laid on what I take to be the two fundamental and controversial premises which support this argument: first, the endogeneity of time-relations involved in financial markets; and second, the revisability of these timerelations. The advantage of recasting Esposito’s position in this way is the defence it enables against various criticisms articulated in theory and philosophy circles, such as those of Ray Brassier. Finally, I discuss the significance of Esposito’s theory, not only for this class of financial transactions, but also for certain issues in the philosophy of time. Keywords Finance, temporality, derivatives, philosophy of markets, Elena Esposito, Ray Brassier Introduction The last decade or so has seen an upsurge in literature on the theoretical foundations of abstract finance and their intersection with questions of philosophy and sociology. Whether driven by vestiges of the 2008 crisis or continued theoretical interrogation of financial models, debates regarding the dynamics of financial markets and their interdependency with financial Finance and Society 2020, 6(2): 114-29 © The Author(s) 10.2218/finsoc.v6i2.5270 Article 115 Finance and Society 6(2) economics continue to engage diverse registers. Donald MacKenzie (2006: 12) asserts the entanglement of academic economics with the life of markets, describing theory as “an active force transforming its environment, not a camera passively recording it”. Elie Ayache, in The Black Swan (2010), The Medium of Contingency (2015), and other texts, makes ostensibly deterministic pricing models contingent, addressing “the recalibration of the derivative pricing model as a radically contingent event” (Ayache, 2016: 205). Building on Ayache’s work, Suhail Malik (2014) analyses this contingency in three forms: the fungibility of what is priced, the variability of price, and the volatility of pricing. Most recently, Timothy Johnson (2016: 202) alludes more broadly to “substantial links” between technical finance and the work of modern philosophers such as Alain Badiou and Quentin Meillassoux, asserting commonalities between distant fields, and providing ample evidence of increased and increasing willingness on the part of scholars to evaluate such links. Relative to these contributions, it might be thought that Elena Esposito’s research in this domain only recapitulates familiar themes already developed more fully by other authors. Following prior research in the social studies of finance (Knorr Cetina and Bruegger, 2002; MacKenzie, 2006), Esposito (2011: 11) considers prevailing theories to lack “circularity” and neglect the bilateral dependency of economic theory and social behaviour. No longer objective, descriptive empirical sciences, for Esposito, economic and financial theory informs expectations about the decisions it purports to describe, and agents reflect these expectations in their own comportment. But, in spite of these commonalities, there remains a protophilosophical kernel of Esposito’s which is an original and additional intervention into the literature on the theoretical foundations of finance. In it, these notions are not only taken over and extended, but also revealed as manifestations of a more fundamental theme: the temporality of the systems in question. Esposito (2011: 9) asks, “Is it possible that the problems of economics that we are faced with at present … have to do with the ways with which time is dealt?” From this perspective, the financial crisis becomes “a matter of oversimplified visions of the future and of risk that referred to the present” (6). Money, interest, risk, and consumption – not only these but also a vast span of other economic and social categories carry camouflaged metaphysical content and, once their occluded temporal dynamic is properly excavated, require revision. Whilst her peers are in no way oblivious to the importance of temporal assumptions in the foundations of finance – indeed, Jon Roffe dedicates an entire chapter to them in Part 2 of his Abstract Market Theory (2015) – Esposito’s work features a particularly sustained engagement with them. This is a distinctive mark of her approach. Esposito’s account is multifaceted and imbues behavioural finance, monetary theory, political economy, and other sub-disciplines with philosophical and specifically temporal import. For one, like Ayache, Roffe, and MacKenzie, she adduces the increasing prominence of the Black-Scholes-Merton option pricing model in the 1980s and 1990s as evidence of the specular dynamics of pricing – in spite, it must be said, of some reticence as to the extent of its actual implementation.1 In the context of theories of price movement, contrary to the hypothesis that causal influences propagate asymmetrically – which is to say that past conditions, such as the variables of which prices are functions, affect the future without being affected in return – Esposito (2011: 22) contends that, “Constraints are not unidirectional, always proceeding from the past to the future, but can instead be understood as multidirectional, proceeding from the future to the past”. Such a perspective figures in her extended development of the notion of revisability (the revisability afforded by the acquisition of derivatives) and in the eponymous thesis which plays a pivotal role in her argument. Further, Esposito shows how growth subjects more and more phenomena to the dynamics of exchange 116 Husbands and valuation, how financialisation replaces utility and custom by market value, and how more and more complicated dynamics come to influence their price. As a result, expectations about price movements count less than expectations about such expectations – a recursive spiral which increases sensitivity to unpredictable swings in market sentiment, introduces additional volatility, and intensifies the prospect of financial contagion.2 Esposito thus attributes the concrete implications of the financial crisis to metaphysical aberrations. The philosophical implications of derivative instruments are thus as diverse as the heterodox claims which show up in The Future of Futures are provocative. The academic response to Esposito’s work is less than commensurate with the stature of these claims, which defy the tendency for philosophers of time to operate at a distant remove from the preoccupations of the everyday. The Future of Futures bears directly upon present economic and political quandaries, reaching their apex in the aftermath of the crisis. Despite this, a limited amount of relevant commentary has arisen. Esposito’s claims are addressed in Malik’s 2014 extended essay on ‘The Ontology of Finance’, which draws heavily upon her discussion of ‘time-binding’ (see Esposito, 2011: 18-37).3 Malik uses this to ground his own account of finance’s generation (or ‘inscription’) of ontological contingency. Esposito’s ideas also inform the early work of Jens Beckert (2014) in this area and feature prominently in Ray Brassier’s 2017 seminar paper, ‘Pricing Time’. In none of these, though, is the specifically philosophical import of Esposito’s innovation examined for itself. In view of this hitherto modest response, this article aims to formulate clearly the most important metaphysical tenets of Esposito’s position, and to subject them to critical review in the context of the philosophy of time. In the course of this analysis, Esposito’s argument (spread over hundreds of pages in the original and embedded in extended quasi-historical discussions of the role of money, the financial crisis, and the nature of instruments such as derivative securities) is formally reconstructed. Two propositions are identified as contributing much of the metaphysical content of Esposito’s approach: first, her Endogeneity Thesis, which asserts that temporal relations and determinations are system-specific (a thesis consonant with broader trends in modern philosophical discussions of temporality); and second, her assertion of the variability of these relations and determinations. For Esposito, the dynamics of a given system (e.g., a particular financial market) are determinative for these relations. They constitute a local time whose relations are independent of global time-relations. Moreover, these relations vary; in particular, they are revisable from moment to moment. The advantage of this formulation of Esposito’s argument, and of drawing attention to these two theses, is not only a gain in clarity and the increased potential this affords for critical engagement on the part of philosophers; it also enables a defence of Esposito’s theory to be mounted in response to objections raised by Brassier in his recent discussion of Malik’s ontology of finance. The article proceeds by first presenting and reviewing Esposito’s argument. After this it develops an analysis of the Endogeneity and Revisability Theses. It then considers and motivates Brassier’s objection to this argument, and in particular his assertion that the rigorously deterministic relations, which govern the markets whose dynamics fall within the purview of Esposito’s analysis, are inconsistent with the Revisability Thesis. A defence of Esposito’s account is then proposed against Brassier’s reservations. This defence casts into clearer relief the advantages of this article’s reconstruction of her line of thought. Endogeneity and revisability in derivative transactions Being diffuse and expressed in a mixture of theoretical registers, it is helpful to extract the 117 Finance and Society 6(2) most important metaphysical propositions from Esposito’s analysis. These present time as a tradable object, as enumerated below. 1) Time-relations are internal to systems 2) Financial systems are comprised of expectations about prices 3) Present future and future present bound the future 4) The present future amounts to expectations (about prices) 5) The future is the revisability of the present future and the future present 6) Derivatives enable the revisability of expectations (about prices) 7) Derivatives sell the future 8) Derivatives transact time Premise 1 is Esposito’s Endogeneity Thesis. It surfaces in a number of guises in the second chapter on ‘Time Binding’, a term coined by Alfred Korzybski then adapted and developed by the sociologist Niklas Luhmann who, like Esposito, considers social and economic systems as embedding notions of time in their behaviour, whether or not accompanied by an explicit “conceptualization” of time (Luhmann, 1991: 34). First of all, the Endogeneity Thesis appears as what Esposito (2011: 23) labels a principle of “temporal relativity”. This thesis can be defined in opposition to a principle of temporal absolutism, namely that time is independent of events or “autonomous”; more fully, “the impression that there is an autonomous time dimension, a time that serves as a stable reference and influences both concepts and attitudes” (Esposito, 2011: 23), rather than concepts and attitudes and any and all contents of this dimension influencing or constituting time. For Esposito, there is no absolute or universal time which might preside over the times of different systems. Some historical context assists in interpreting this position. As an illustration, it can be contrasted with the position of metaphysicians working in the Newtonian tradition such as Samuel Clarke (Alexander, 1956: 105-7), or with the way in which imperial chronometry sought to resolve the flow of time as kept in various regions of empires into a standardised superordinate time: Even a master clockmaker’s finest work would offer only pale reflections of the higher, absolute time that belonged not to our human world, but to the ‘sensorium of God’. Tides, planets, moons – everything in the Universe that moved or changed – did so, Newton believed, against the universal background of a single, constantly flowing river of time. (Galison, 2003: 19-20) Instead, for the tradition Esposito stewards, different systems and the different theories describing them possess different times, which need not be coordinated or subject to common measures: Time is, therefore, seen as a structure of systems, a structure that gives an order to operations and connects them to one another. (Esposito, 2011: 22) Insofar as time is a structure of systems as Esposito declares, time-relations – relations of events, such as are involved in preceding or following – are internal to those systems. The time comprised by the Earth’s rotation about its axis, the series of alternations between day and night, pertain to the dynamics of the solar system and its orbit of the sun, and to the customs and habits civilisation establishes around them. The time comprised by genetic mechanisms which encode the lifecycle of the human organism regulate its growth, decay, and eventual disintegration. The half-life of a caesium-137 nucleus, the gestation period of a tiger, the 118 Husbands transitions between different stages of psychological development, pertain to the incongruous forces which animate each of them for their own part. Esposito denies that the temporal properties of these systems and processes – the position of the constitutive events in time, or the relations of these events to each-other, being-before or being-after – are reducible to a common set of temporal properties. It is in this sense that her writings repudiate absolute time as superfluous. These remarks express Esposito’s thesis of endogeneity. As this article will show, this position unlocks the broader philosophical insight to be gleaned from her analysis of financial markets; it allows the labyrinthine trade in financial instruments and abstract derivatives to constitute their own system of time. Premise 2 is definitional and qualifies the scope of Esposito’s analysis. The system whose time dynamics are in question is the financial system and, of particular interest, the voluminous market for derivative instruments (CDOs, interest rate swaps, VIX futures, etc.). What is most meaningful (and controversial) about this premise is the subject matter upon which her discussion fixes. The characterisation of this system in terms of expectations is prima facie arcane, clashing with more familiar motivations couched in such terms as the infusion of liquidity, provision of credit, transfer or hedging of risk, inter alia. Why reify expectations? Esposito’s rationale is that the transactions which comprise this system contemplate less the characteristics of the underlying subject matter (whether a resource such as a bulk commodity, an interest rate, or performance of a loan) from which a derivative derives, or the referent of the instrument traded, than it does traders’ expectations about price movements. The forces driving these transactions are not objective characteristics of the goods, the subjective utility of the underlying to a consumer, the discounted value of future cash flows derivable from them, or their production cost adjusted for a required return. Rather, and contrary to traditional doctrines about price levels such as efficient market hypotheses (in which they reflect complete informational availability), Esposito holds these to be functional on expectations – in a dual sense, not only the sense in which participants’ views on pricing adequacy are informed by their stance on what the consensus price will be at a future time, but also the second-order sense in which, given that price levels prevailing at any given time reflect expectations and that prices are set within a market, taking positions presupposes forecasting future prices and thus future expectations, producing a highly circular trading environment. She posits accordingly: Although markets have always had their dynamics, which are led by the mutual observation of observers, this observation has now become the real object of transactions. (Esposito, 2011: 95) To the extent that a set of pricing dynamics produce the salient features of the financial system, these remarks lend support to Premise 2, which is extended later in Esposito’s argument. With her next two premises, Esposito most explicitly veers into the terrain of temporality. Premise 3 posits a familiar distinction between the future present and the present future: The uncertainty of the future is expressed by the fact that the future price of an asset does not coincide with the expected value of the future spot price. In other words, the future price in three months is not the same as the expected price of the asset three months later … The estimate of risk marks the difference between these two prices. (Esposito, 2011: 136) Here, Esposito’s distinction appears as a distinction between expectations and reality: the present future is the future we expect, the future present the future that will be. Similarly, elsewhere she refers to the present future as “our current anticipation of the future” and the 119 Finance and Society 6(2) future present as among “the presents that will become actual in the future” (Esposito, 2011: 23-24). Importantly, though, Esposito’s formulation of this distinction centres on uncertainty, whether reflective of epistemic limitations or ontological indeterminacy. In bounding the future by present future and future present, as per Premise 3, Esposito defines the future as an oscillation and interchange between these two modes of time: the future is the iterative formation and revision of expectations. Brassier, in his commentary on Esposito’s work (through the prism of Malik’s 2014 essay), offers his own succinct definition: The distinction between the present future … is ‘our current anticipation of the future’ and the future present … the ‘present that will become actual in the future’. (Brassier, 2017: 95) The present future, as expected, is inactual; the future present becomes actual. Further, Premise 4 is a definition which follows readily from the foregoing, subject to the clarification that the subject matter of Esposito’s analysis is, once again, financial markets together with what she takes as the most important variable which encodes their dynamics, namely price levels. As will be explored more fully when Brassier’s own critique is developed, one immediate consequence of this proposition is its suggestion of idealism, insofar as Esposito’s position contemplates expectations about prices, rather than prices themselves. Expectations are subjective or, at best, intersubjective, yet price movements are (it would be thought) objective. A possible loss of generality is implied by this framework, then, in spite of its increased precision. Sections two and three address this concern in more detail. Premise 5 provides a definition of Esposito’s esoteric usage of the term ‘future’, which modulates frequently, as can be observed in the distinction between present future and future present. For Esposito, this term refers to neither of these two – nor indeed to the distinction between what is actual or inactual, which she takes over from the work of Luhmann – but rather to revisability, and to the difference between present future and future present. How can we make sense of this definition, and what is gained by couching futurity in terms of revisability? The following passage provides further elaboration: The temporal integration of the system (the fact that the different presents all belong to the same time) is not given once and for all on the basis of the fact that the past precedes the future, but is instead continuously produced and revised as time progresses (the constraints introduced in the present are subsequently revised in the context of a control that evaluates and corrects them, but remembers their past sense). The future redescribes the past in accordance with how it remembers the way in which the past present had projected its future, and recognizes itself as the future of that past, as a different perspective inside the same time (selections have an order, and that, as we have already stated, is what time is needed for). (Esposito, 2011: 27-28) These remarks not only help develop the notion of revisability, but also contain much of Esposito’s metaphysics of time. A number of distinct theses can be derived from them. First of all, from the fact that the past precedes the future it does not follow that the past determines the future. The denial of this logical relation opens a distinction between the temporal order of events and the order in which they are determined, or in which the “temporal integration” of which Esposito speaks is established. Not only the outcome predicted by past expectations, but revisions made to past expectations about the value of a security, govern the evolution of its price in time. As much as the bubble of credit which proliferated in the subprime mortgage market preceded the 2008 financial crisis, this bubble was only determined as such, determined as a bubble, after the emergence of widespread defaults. Whatever conditions may have prevailed in the past of 2008, the months and years prior to the 120 Husbands crisis, the overvaluations and price corrections, then inconceivable for all but a select few adepts, it was only with the cascading revisions to collective expectations, then a singular future event, that this outcome was determined. Secondly, this temporal integration of the system, consisting of the relations which bind moments together, and in this sense “the fact that the different presents all belong to the same time”, such as sets of events connected by natural laws or economic theories which describe them, is itself variable. Being at a given position in time, or occurring before or after another event, is a mutable predicate. Indeed, it is in this sense that time itself is subject to time, such as would be the implication of the claim that temporal integration occurs as time progresses. Lastly, with the contention that “the future redescribes the past”, not only the structure of time, such as the order of events and the order of their determination, but also the very contents of time are revisable: the future “recognises itself as the future of a past” and generates the past which is consistent with it, just as, following Esposito’s example, fashions appear and disappear discontinuously, bringing with them immanent criteria which cast previous fashions in different lights. As revisions are made to the interpretation of market events required for the formation of expectations, new phenomena are revealed not present before, and previous observations recede into insignificance. These are, therefore, the three senses in which Esposito characterises the future as revisability: first, the fissure of the order of events and order in which they are determined; second, the variability of time-relations themselves, whether cardinal or ordinal; and third, the contents of time, events with their qualitative peculiarities and haecceities, varying in time. This ostensible abstraction in fact provides a crucial link to Esposito’s central metaphysical thesis, concerning the temporal effects wrought by the transaction of derivatives. As will be shown in the following analysis of her remaining premises, it is owing to the power of derivatives to allow expectations (the reciprocal expectations of observers) to be revised, that such effects can be exerted. Derivatives pertain to time because they pertain to time qua revisability. Nonetheless, there is a lingering opacity to these propositions, which stand out as the metaphysical apotheosis of The Future of Futures, invoking temporal predicates, determinations of cardinality and ordinality with respect to time, and other unintuitive notions. Much of this can be dispelled with Esposito’s quite concrete and quite simple examples and illustrations – which serve not only as examples and illustrations, but also as logical grounds of Premise 6. Derivative securities, in Esposito’s framework, pertain to expectations. How might this claim be explained and developed? Firstly, this framework breaks with traditional accounts of these securities’ purposes, such as the provision of liquidity or the hedging or transfer of risk. As Malik (2014: 629-36) observes, in contradistinction to the somewhat outmoded staging which surfaces and resurfaces in academic economics (such as impecunious farmers purchasing forwards to protect themselves from wheat price fluctuations, or SMEs exposed to exchange rate volatility entering into currency swaps as an offset), the volumes of derivatives traded, measured either by notional or marked-to-market values, dwarf the volumes explicable by non-speculative motivations (Hull, 2002: 71). These theories thus hardly suffice to explain the market dynamics associated with these securities. However, a more important contrast to draw for present purposes follows from the fact that the temporal and therefore metaphysical implications of these dynamics remain obscured by such explanations, suggesting the need for more thorough excavation. Esposito (2011: 110) observes in this vein that “most derivative contracts close without the exchange of anything more than the mutual observation of 121 Finance and Society 6(2) observers and their expectations” – not as if to deny that such contracts are ultimately financially settled, but instead to assert the following: rather than the underlying commodity which would be the putative object of such trades being exchanged at the settlement of a contract, it suffices for the difference between the spot price of the underlying and the strike price of the option, or forward price of the forward (mutatis mutandis for other instruments), to be remitted in order for any and all obligations assumed in them to be discharged. This difference is a difference between prices, and thus a difference between prices which themselves reflect anticipations about price movements, rather than demand, or intersubjective utility. Derivatives transactions are thus settled based on expectations about future expectations: “Although markets have always had their dynamics, which are led by the mutual observation of observers, this observation has now become the real object of transactions” (Esposito, 2011: 95). Far from being an aberration, speculation is seen to be intrinsic to markets. These considerations connect readily to the notion of revisability, which features in Premise 6 and can be used to furnish a more formal justification of this premise. Consider a derivative D which derives from an underlying U. The expectations of a market participant (as a potential acquirer of D) may peg the underlying’s spot price at given time t at a level P. In Esposito’s terms, P amounts to the present future price of D. Now, all of the multifarious ramifications of this participant’s expectations reflect P – the willingness to trade U in the present, the ability to take actions which might depend on the availability of U as an asset or a resource, or the implications of P for other variables. With the arrival of the future present, though, P may not obtain, but some other price PF. What is the specific relation of derivatives trading to this complex? “What is traded on derivatives exchanges is not the future given (the then unknown strike price of the underlying) but the present risk of that price against the delivery price” (Malik, 2014: 713). Derivatives trading allows the increase or decrease in, the magnification or nullification of, or the losing or profiting from this difference between P and PF (‘risk’ or ‘uncertainty’ in the terms of Esposito and Malik). Their subject matter is therefore precisely this difference, the risk and uncertainty posed by it, and their function is precisely its management or exploitation. For instance, combinations of options which form a straddle4 at a given price level promise to compensate the purchaser for any price fluctuation of sufficient magnitude, positive or negative, in exchange for a premium (inversely related to the magnitude required), potentially enabling them to comport themselves as if indifferent to such price movements, or to profit or lose from them. In sum, derivatives concern expectations; these expectations in turn concern the expectations of others, forming a collective whose interdependencies constitute the market and determine price levels. As Esposito neatly summarises: Derivative instruments are used to manage the difference between the present future and the future presents in the present, between what one can expect to happen tomorrow, today, and what will actually be achieved tomorrow, as a result of what one does today in order to prepare for it. Derivatives allow one to make decisions today that affect the way the future will be, while preserving the freedom to decide one way or the other when this future will be present. (Esposito, 2011: 105) The revisability of participants’ expectations, constituted by the difference between the present future and future present, is in this sense what is enabled by the acquisition of derivatives couched in this difference. This is the rationale for Esposito’s Premise 6. By way of further illustration, Esposito offers as a case example the Black-Scholes-Merton pricing model. Researchers in the field of financial engineering, aiming to develop quantitative tools for the pricing of options, had been beset by the conundrum as to how the future prices 128 Husbands In this sense, economic history can be seen as a series of folds, or structural distinctions: from things to private property to money to derivatives. (Frankel and Ossandon, 2013: 277) The metaphysical import of these developments in financial markets, then, outstrips the already problematic reality of extreme volatility, financial crisis, and resultant collective immiseration. They impinge upon the time proper to these markets since the foci of the transactions, being revisions to expectations, are time-relations themselves, “built as a mirroring of possibilities that open and close where the future includes a future present from which I can look at my present as past” (Esposito, 2011: 27). In this way, Esposito’s research provides a new lens for investigating the foundations of financial society and derivative finance. Whilst scholars working on the foundations of finance in the last decade have without a doubt unearthed significant metaphysical content latent in its theoretical assumptions – from the contingent (in)accuracy of pricing models, to the interrelation of theory with actual trading – the revisability of pricing proposed by Esposito, originating in participants’ expectations, entails new metaphysical conclusions about time, and illustrates how time is fashioned into a tradable object. As Esposito concludes, the task which confronts researchers and theorists working in these domains is to cognize, rather than to efface, the circular and self-referential characteristics of markets which serve to proliferate these derivative instruments. For philosophers, a different conclusion obtains. Whether or not through academia, implicit metaphysical beliefs about time intermix with real actors’ decision making, producing tangible ramifications, making the peculiar time-dynamics of the systems involved urgent objects of philosophical enquiry. Quite to the contrary of Marx’s dictum from Theses on Feuerbach, in which philosophy contributes only interpretation and never concrete change, these time-dynamics, uninterrogated, become the very impediments of such change. Notes 1. Esposito (2011: 9): “The formula only worked so well because, for a certain time, volatility adjusted to the estimates of the formula, not because it predicted the actual movements of volatility”. 2. This aspect of Esposito’s presentation follows the extensive analysis of reflexive and recursive market expectations given in Soros (1987). 3. It must be acknowledged that Esposito’s discussion of ‘time-binding’ is, in turn, drawn from the work of Niklas Luhmann (1981: 126-50; 1991: 51-72). 4. 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