Abstract Market Theory

Jonathan Roffe

• Publisher: Palgrave Macmillan
• Year: 2016
• Print ISBN: 9781349552795, 9781137511744
• eBook ISBN: 9781137511751
• Topic: Philosophy
• Subtopic: Econometrics

Financial markets play a huge role in society but theoretical reflections on what constitutes these markets are scarce. Drawing on sources in philosophy, finance, the history of modern mathematics, sociology and anthropology, Abstract Market Theory elaborates a new philosophy of the market in order to redress this gap between reality and theory.

Part I

The Being of the Market

1

Probability and Contingency

Ayache and the case of derivatives – Brief history of the formalization of derivatives pricing – The orthodox image of derivatives pricing – The ubiquityof black swans – First critique, from Meillassoux – Second critique, from Deleuze and Bergson – Third critique, from the integral redundancy of the market on the orthodox view – Summary

Ayache and the case of derivatives

To begin with the obvious: there are many markets, and many kinds of markets. It would be easy to insist as a result that the use of the indefinite article in ‘the market’ is nothing more than a matter of convenience, and that any attempt to elaborate a theory of the market in the singular is bound to fall into either triviality, overgeneralization, or both. Perhaps.

Here, drawing on the work of Elie Ayache, we will begin by considering a single case, the ensemble of markets in which the financial instruments known as derivatives are traded. Now, even though it is clear that this decision is supported by the axiom of inclusion presented in the Introduction. On the other, it appears a strange, even perverse choice; for, unlike the market in oil, or the country stall that sells bananas, derivatives markets are often presented as dealing with a confected object with at best tenuous links to ‘reality’. While the argument of these first two chapters is that a rigorous consideration of the nature and functioning of derivatives is the royal road to the theory of the market, for the moment – since derivatives are unequivocally and entirely of the market – it is legitimate to begin the investigation here and rigorously follow its consequences.

According to a patent legal definition, a derivative is any contract ‘whose value is based on the performance of an underlying financial asset, index, or other investment’.¹ That is, a derivative is any financial instrument whose price is indexed to the price of something else – their price derives from that of the underlying. At their most basic, derivatives take three forms. The first, options, provide the owner of the contract with the right to act – to buy (call options) or sell (put options) in the underlying market at a set price (the strike price) and a set time in the future (the time of expiry or exercise). The second is forwards, according to which the owner is obliged to purchase the underlying at the strike at expiry. Finally, there exist swaps, which allow their owner to swap one underlying for another.²

Three further features are characteristic of derivatives. These contracts, first of all, rather than being simply held and executed, are themselves traded in their own markets. There are thus (at least) two markets whenever derivatives are being traded: their own and the market in the underlying to which they are related. Second, given that at root derivatives are contracts for (at least the license to engage in) future action of some kind, they can in principle be varied in an unlimited number of ways. The three varieties noted above, sometimes called ‘the vanillas,’ thus give way to a panoply of more complicated cases. In the next chapter, we will consider collateralized debt obligations (CDOs), which played a central part in the subprime crisis of 2007–8. A more straightforward example is that of barrier options. Like regular put or call options, they allow for the purchase or sale of the underlying at the strike upon expiry. However, they also include provisions (‘barriers’) according to which they are voided before that time – for example, if the price of the underlying falls below a certain threshold. It is this feature that makes derivatives problematic from the point of view of regulatory policy.³ Finally, any derivative can become the underlying for a higher order instrument. We see then that derivatives vary not just in terms of the complexity of the contract in question, but also in terms of the hierarchical relationship that can hold between the initial underlying and the derivative in question.

While these more complex cases are of relatively recent mint, derivatives have existed for a long time indeed. The first significant recorded case is found in Aristotle’s Politics. There, he recounts how Thales, convinced by certain astronomical speculations, made a series of down-payments on olive presses, which he then rented out, profiting from the bumper olive crop.⁴ These rental contracts were, in the sense noted above, futures. Many other examples – both quotidian and infamous – could be enumerated, but what is more significant are two developments that took place somewhat more recently, and that fall under the heading of the mathematization of finance.

Brief history of the formalization of derivatives pricing

The first of these is found in the doctoral work of Louis Bachelier, submitted in 1900 under the title ‘Théorie de la speculation’.⁵ Bachelier’s goal was to ground the analysis of price movements in the French stock market in mathematics, and to this end effectively invents the mathematical theorization of probability calculus. While Bachelier’s position is interesting in a number of ways, here his most significant claim is that price movements are stochastic, which is to say, statistically random in character. For Bachelier, there is no fundamental law governing the fluctuations of price on the market; consequently, the only knowledge that may be gained about future prices is by way of probabilistic analysis.

Now, Bachelier’s thesis also includes a theory for the pricing of options, which is to say, a mathematical means for predicting the price of a derivative at a given time and under certain conditions. While in many respects his account is continuous with pricing models used now, Bachelier makes a number of presuppositions about the nature of price movements in the underlying model that were consequently problematized to a significant degree.⁶

The second concerns of interest here is the moment of the refoundation of the kind of model presented by Bachelier, developed in two now classic papers in the early 1970s by Fischer Black, Myron Scholes and Robert Merton.⁷ The model these papers developed would later garner Black and Scholes a Nobel price in economics, and is known as the Black-Scholes-Merton pricing model, or BSM.

BSM, a partial derivative equation, allows for the calculation of the price of futures and other derivatives. It has five variables: time to expiration, current price of the underlying, the strike price (contracted price of the derivative at expiration), extraneous charges like interest rates, and the implied volatility of the underlying. The structure of BSM will become more significant later in the argument, but for the moment note that, bar the last variable, these values are easily and uncontroversially obtainable – in the final analysis, BSM is a means to articulate the price of the derivative and implied volatility. In its orthodox acceptation (to be somewhat problematized in what follows), implied volatility is a measure of the degree of likely variance in the price of the underlying. It is thus the mark of the implied consequences of the trade of the underlying for the price of the derivative under consideration.

The orthodox image of derivatives pricing

Now, while the BSM pricing model is afflicted with a variety of problems, some of which we will consider shortly, it is important to emphasize, not only that it remains (however modified) the central touch point for the modelling of derivatives prices,⁸ but also that the bulk of contemporary pricing models share with it the same basic features. Three of these, taken together, constitute what we will call the orthodox theory of derivatives pricing, a set of foundational assumptions. These are as follows:

1)derivatives markets are stochastic processes: that is, they involve a random series of events;

2)these processes can therefore be mathematically modelled, providing us with a calculus of the likelihood of a range of future states of the market in question;

3)these mathematical models are probabilistic in character.

All three of these basic features appear completely uncontroversial from the point of view of options pricing, both in theory and practice. That this is the case, though, is not to be taken as proof that they are correct; for, in fact, they mark the philosophical foundations of options pricing, and are thus subject to philosophical critique. Following Ayache, we will see that the third of these assumptions is dramatically problematised by three critical arguments, arguments moreover which will require a decisively stronger formulation of the first assumption, such that it will no longer be compatible with the other two.

The ubiquity of black swans

Before considering these arguments, and in order to mark out their scope, we must consider and put aside what is perhaps the most well known critique of the orthodox view: that advanced by Nassim Taleb in The Black Swan.⁹ In this book, Taleb, himself a former derivatives trader, addresses what he calls ‘highly improbable’ events – the titular swans – such as the global financial crisis. Such black swans have, he argues, three characteristics as events. They are first of all ‘outliers [ ... ] because nothing in the past can convincingly point to its possibility’. The second characteristic is qualitative: black swans have an ‘extreme impact’. Finally, while, such events cannot be predicted in advance, they are subject to what Taleb calls ‘retrospective predictability’.¹⁰ His central claim, entirely of a piece with Humean scepticism, is that the human mode of existence is such that we inevitably tend to downplay the likelihood of such events. Consequently, options pricing models such as BSM can only cultivate a kind of hubris, a certain kind of disaster blindness or epistemological fragility. Rather than blindly trusting such predictive tools, Taleb counsels that we must cultivate an epistemological modesty and attention to our limits, a deliberate anti-fragility.¹¹

This invocation of Hume is not incidental. If we consider adherents of the orthodox view on the one hand, and Taleb on the other, we find ourselves presented with precisely the split between dogmatic rationalism and dogmatic scepticism that opens Immanuel Kant’s Critique of Pure Reason. From the first point of view, one that is adopted by the full range of agents in contemporary finance, there is no fundamental error in conceiving of the pricing of derivatives in this way, a way that provides a more or less reliable prediction of price movements. From the second, the model dramatically undersells our incapacity to consider all of the relevant factors that will come to bear on future states. What is shared by both, though, is the commitment to the probabilistic framework itself. In other words, adherents and detractors in the style of Taleb only disagree about the second assumption of the orthodox model: that is, its capacity to predict future outcomes, while agreeing that probability is the correct theoretical terrain. The black swan is a probabilistic animal, an animal of likelihood and relative scarcity. Its two taxonomers merely disagree about the degree of scarcity in question.

It is here that Elie Ayache’s work must be introduced, and a first aspect of its importance demonstrated: for Ayache’s project is no simple analogue but the same project pursued by Kant, albeit on a different level of application. The Blank Swan repeats this point at numerous junctures: ‘Probability theory is bad for the market as it eventually leads to the metaphysical extremity of the CDO and to the blanket rejection of all probability models by someone like Nassim Taleb’ (BSEP xv). In other words, there are two general positions that arise in the theory of the market if the category of probability is taken as foundational. The first is a dogmatic position that considers every market outcome to be in principle thinkable. This position is exemplified by those who took collateralized debt obligations (the CDOs whose status will be discussed in the next chapter), despite their immense complexity, to be subject to pricing like any other derivative. Like Leibniz and Wolff, the advocates of CDOs, for Ayache, found themselves outside the legitimate scope of their claims on the nature of reality, unable to orient themselves in ‘a wide and stormy ocean, the native home of illusion, where many a fog bank and many a swiftly melting iceberg give the deceptive appearance of farther shores, deluding the adventurous seafarer ever anew with empty hopes, and engaging him in enterprises which he can never abandon and yet is unable to carry to completion’.¹²

The second is the sceptical position, according to which certain future outcomes, being radically unknowable, should be taken as proof that the belief that the advent of certain outcomes, as indicated by the calculus of probabilities, is illusory at root. This position is, as Ayache suggests, Nassim Taleb’s. As it happens, though, all of Taleb is already to be found in the third part of Hume’s Treatise of Human Nature, ‘Of Knowledge and Probability,’ and his admonitions directed at the dogmatic pretensions of traders resembles nothing as much as Hume’s account of the ‘mixture of truth and falsehood in the fables of the tragic poets’,¹³ who are emblematic of the dogmatic rationalists. For Taleb, as for Hume, all knowledge of the future is conditional on the habitual expectations that constitute the human mode of being in the world, and these habits involve a congenital blindness with respect to what is unexpected. Consequently, to think that pricing models are a reliable means of prediction is to be under the sway of a kind of manic delusion: that every future event is within the scope of human reason and can be known in advance. To trade in derivatives is to dance well beyond the circle of firelight, in a night whose blackness contains monsters unknown and unknowable but for the dramatic consequences of our encounters with them.

Like Kant, Ayache will make two key interventions into this opposition. The first is that, as we have seen, both views are based on the same assumption of the probabilistic framework, and that what is required is to critique this framework itself. The second is that both positions are in part correct – and more correct than they know. The sceptical position is right to insist on the unpredictability of future states, not occasionally (as is Taleb’s view) but absolutely and in general. This is why Ayache will – quite rightly – describe his project as a ‘transcendental philosophy of the Black Swan’ (BSEP 28). Conversely, the dogmatic orthodox position is right to insist on derivatives markets as stochastic in character; it is also right to posit a certain role for probability calculation, even if it mistakes the status of this calculus and what grounds its effectiveness.

We see then that Ayache’s project is in every way a cas...

Table of contents

• Cover
• Title
• Introduction For an Abstract Market Theory
• Part I  The Being of the |Market
• Part II  Realization of the |Market
• Notes
• Works Cited
• Index