The Blank Swan: The End of Probability

By Elie Ayache

October 19th 1987 was a day of huge change for the global finance industry. On this day the stock market crashed, the Nobel Prize winning Black-Scholes formula failed and volatility smiles were born, and on this day Elie Ayache began his career, on the trading floor of the French Futures and Options Exchange.

Experts everywhere sought to find a model for this event, and ways to simulate it in order to avoid a recurrence in the future, but the one thing that struck Elie that day was the belief that what actually happened on 19th October 1987 is simply non reproducible outside 19th October 1987 – you cannot reduce it to a chain of causes and effects, or even to a random generator, that can then be reproduced or represented in a theoretical framework.

The Blank Swan is Elie's highly original treatise on the financial markets – presenting a totally revolutionary rethinking of derivative pricing and technology. It is not a diatribe against Nassim Taleb’s The Black Swan, but criticises the whole background or framework of predictable and unpredictable events – white and black swans alike - , i.e. the very category of prediction.

In this revolutionary book, Elie redefines the components of the technology needed to price and trade derivatives. Most importantly, and drawing on a long tradition of philosophy of the event from Henri Bergson to Gilles Deleuze, to Alain Badiou, and on a recent brand of philosophy of contingency, embodied by the speculative materialism of Quentin Meillassoux, Elie redefines the market itself against the common perceptions of orthodox financial theory, general equilibrium theory and the sociology of finance.

This book will change the way that we think about derivatives and approach the market. If anything derivatives should be renamed contingent claims, where contingency is now absolute and no longer derivative, and the market is just its medium. The book also establishes the missing link between quantitative modelling (no longer dependent on probability theory but on a novel brand of mathematics which Elie calls the mathematics of price) and the reality of the market.

• Language: English
• Publisher: Wiley
• Release date: May 5, 2010
• ISBN: 9780470661765

Book preview

Introduction

This is a book about writing, pricing and contingent claims. I hold that the writing process and the pricing process are two special kinds of processes that do not take place in possibility or in probability, like the traditional stochastic processes. They fall completely outside prediction. As processes, they keep re-creating themselves and differentiating themselves, yet they do not unfold in chronological time. For this reason, their Swan bird, or the event that gives them wings, is BLANK. It is neither Black nor White; it is neither loaded with improbability nor with probability. It can only be filled with writing, as when we say ‘to fill in the blanks’.

Likewise, the medium of contingent claims - that which transmits them and translates them into prices - is something I call the market. This cannot be covered by probability theory or derivative valuation theory. The medium is of the nature of writing, and the trader of contingent claims is a writer and a creator. He doesn’t predict the market (or its generalization, which is history) or try to anticipate it. The market is his work, as when we say that the book is the work of the writer or the poem is the work of the poet.

It was during the period in which I was an option market-maker on the floors of LIFFE (London International Financial Futures Exchange), in 1990-95, and MATIF (Marché à Terme International de France), in 1987-90, that I learnt what it really meant to be a market-maker, or a ‘local’ (as we say), and how far the open outcry market (which is the only true form of market to my eyes and the only place where contingency, as a meta-probability, can truly strike) can be from the masquerade and total degeneration of probability to which we were recently led by the Collateralized Debt Obligation (CDO) blunder and the subsequent rout, and will be led by any other form of complex derivative that we cannot calibrate to the market. I believe this whole branch is going to drop off the tree, and the only way to reconstruct a market and return to the market is to go back to the place (and probably the times) where individuals (locals) make the market, as opposed to big institutional players who never understood how to make money in the market in the first place.

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, author of The Black Swan. I think the real intellectual scandal that the whole ‘culture’ of the market is facing today is that traditional financial theory can only understand profit in the market through an imperfection of some kind or other: either by an arbitrage opportunity, or asymmetric information, or monopoly, or Knightian essential uncertainty, etc. (not to mention sheer luck). What is lacking is an account of how to make money in the market as a perfect medium of contingency, not as an imperfect case of probability theory.

Apart from rebuilding a market that may emerge as a true vehicle of speculation (in the good, almost philosophical sense of the world), i.e. as technology of the future, I believe that a critique like the one I undertake in this book can revolutionize the philosophy of probability. Indeed, it is not in probability (or worse, by luck) that money shall be made in the market, but outside probability, in a medium and continuum that I can find no better way to describe than to compare it with the medium of the creation of literary work.

The reason why my book is called The BLANK Swan is that it is not the opposite of The Black Swan as a hasty critic of Taleb’s book would tend to think. The White Swan would be the opposite of The Black Swan and Nassim himself, in a characteristically witty passage of his own book, considers the possibility that somebody some day would write a diatribe against him with the title The White Swan.

My book is not a direct criticism of Nassim’s; therefore it is not opposed to it in colour. Rather, it criticizes the whole background or framework of thought in which one would assume that Black Swan and White Swan are opposed to each other.

The Black Swan is the perfectly unexpected event; the White Swan is the perfectly expected event. Underlying both is the category of prediction and prevision, which is the real object of my criticism. The Black Swan refers to something we cannot see or foresee (it is black) and the White Swan to something evident and clear. Although opposed, the two are predicated on the idea of content of vision, or content of mind, or content of expectation.

My observation is that Black Swans are said to be unpredictable only insofar as the framework and whole register of prediction is maintained. For instance, Nassim’s book is crammed with the framework of prevision, only he argues that there is something - the Black Swan - that typically evades that framework. My criticism consists in suggesting that if Black Swans constantly evade prevision, as Nassim warns us, then we should be able to define them and deal with them completely independently of prevision. Why even keep the framework of prevision when we keep talking of something that constantly evades it?

Like I said, Nassim has to maintain this framework (of prevision) because this is the stuff his book is made of, or the stuffing his bird is filled with, only negatively so. In other words, they are full of prevision, only Nassim constantly argues against it. What would become of Nassim’s book and the whole concept if prevision was eliminated altogether? What if we completely eliminated the content of vision, i.e. both the colours White and Black? What if we eliminated the whole context of colour and of content? Hence the BLANK Swan.

It is not with prevision (either of Black or White) or prediction that we should deal with the Black Swan or define it, but with something else, which, in the course of my book, turns out to be writing and whose quantitative avatar is the market. Writing is something we produce without previous knowledge or prevision or prediction. Writing is quicker than thought and vision. It is a material process, when vision and prevision are only conceptual. Writing transpierces the page it is marked on. It is real. It is a process that eventually transports us to the future, making us attain and fulfil our promises (think of the derivative payoff as a promise that the seller of the derivative has written to the buyer), yet at no point is it based on prediction or forecast.

The market, whose other name is the ‘pricing process’, is such a process. Hence my idea is that the market (or writing) should be the way we deal with Black Swans, not the place where we complain helplessly against them (as Taleb does).

Taleb famously declares that he now belongs to the exclusive ‘club of single-idea people’.¹ These are people who realize one day that they have been carrying a single idea all along in their heads, and this is when they start writing books about it. Taleb’s single idea is that our idealization of the world, what he calls the ‘Platonic’ (theoretical representations, models, schemas, classified patterns, or more generally well-organized knowldege that we see with the eye of our mind), keeps rising to the surface, systematically hiding from our sight the underlying intractable and nonrepresentable reality. ‘It is why we do not see Black Swans,’ he writes, ‘we worry about those that happened, not those that may happen but did not.’² The consequence for the reality known as the ‘market’ is that no Platonic form, no formalization of the unpredictable, or, technically, no probability theory or model, shall ever apply to it.

Single and simple as this idea may be, I say it is still composed of two parts: probability and the market. One can further simplify the idea by eliminating one of the parts. The idea I defend in this book is that the market should replace probability. Thus I end up with the market as the only part and only idea.

The reason why probability or prediction doesn’t apply to the market isn’t that the market is too complex or too human or too chaotic. The reason is simply that the market should be the alternative to prediction in matters relating to the future. It remains to say, of course, how we can relate to the future outside prediction. Trying to answer this question is the stuff my own swan is made of.

Part of the difficulty is that if the market remains single, with only itself to apply to itself, then the apparent tautology will dazzle the thinker and will prevent him from discerning the difference and the differential meaning of the market. Saying that the market is the only way to predict the market, or that immersion in the market is the only way to relate to the future of the market, hardly seems informational. By contrast, my argument would have been more compelling and much riskier if I had contended that the market is the technology, not only of its own future but of the future at large, and that the mathematics of price - which I hold should replace the mathematics of chance and probability - consequently apply to all kinds of historical events, those belonging to the future of the market as well as to the future of humanity. After all, Taleb has written about the role of chance in the market and in life, as the subtitle of his pre-Black Swan book indicates.

I will not be nearly as ambitious in the present book. I will limit myself to the market and to the analysis of contingency as it takes place there (the contingency of market prices - what else? - which, fittingly enough, are the prices of contingent claims). When I take up topics of seemingly broader scope than the market (such as philosophical speculation in Part II and literary creation in Part III), I will always refer them back to the market or to my personal experience as a market-maker or market technologist.

I will stick with the uniqueness and the singularity of the market (which constitutes the singularity of my subject), but will extract my differential meaning from sharp distinctions I will have to make within the strict field of contingent claims and of their pricing technology - distinctions not necessarily visible to the naked eye, such as between possibility and contingency, prediction and writing, derivatives and contingent claims, virtual and possible, etc.

Contrary to history or life, the market possesses a single metric: the up or down movements of market prices. This can be a source of confusion and oversimplification, and is probably the reason why we import numbers from a foreign field, probability theory, in order to account for the numbers in the market. However, this coincidence in numbers can also be a blessing, as it eventually allows us to frame our criticism of probability and prediction with all the greater precision, provided the distinctions I listed above are made.

It is those distinctions, rather than the singular occasion that made me realize them (the market), that will stand ready for generalization to fields that may be strictly superior to the market, either in scope or importance or degree of human concern. In this way, it will truly appear from inside, from the internal difference that the market is in itself quite independently of the things of different scope and different order to which it may later be externally compared, that the market is indeed a general category of thought that surpasses the strict acceptation of the financial market. It is no wonder, from this perspective, that I should draw heavily on the work of philosophers of event and difference such as Bergson, Deleuze and Badiou.

Perhaps the main distinction on which the whole book hinges is the one between possibility and contingency, or, correlatively, between the (theoretical) value of a derivative and the (market) price of a contingent claim. This distinction becomes clearest in the last part of the book, thanks to the conversion, and the three preceding parts can be read (or listened to) as different voices or different variations on the same theme, leading to the final movement, like in a symphony.

In a sense, the three parts say the same thing; they are three voices of the market that do not equivocate on its notion. On the contrary, they say the market in the same sense. Univocity of the market and of contingency is indeed the main theme of this book.

The three preparatory parts are different approaches and travel towards the culmination of the book which appears, in the final part, to be the genesis of the market. Think of the three parts as occurring in the context of discovery and of the concluding part as taking place in the context of justification.

In Part I, the totality of themes is introduced. In Part II, contingency is given a firm philosophical basis (even an absolute status), which will secure the way to think of it independently of possibility, even independently of thought itself.

Part III is literally a travel to the ‘land of the market’. It traverses at once all the relevant spaces: geographical, literary and the space of the book itself. In fact, it is a narrative adventure or a kind of reverie, which the strictly mathematically or philosophically inclined reader may wish to skip at a first reading. Nonetheless, it is the part I personally prefer and in which I have travelled the farthest I could. There are outer reaches in this exploration that even I do not yet quite understand.

Part IV is the promised land, or the new world finally reached. It illuminates the whole book like a beacon. If the reader isn’t afraid of travelling at infinite speed, as Deleuze would say, and of discarding, right at the entrance, any prejudice or preconceived idea he may have about the pricing of contingent claims and their market, he or she is welcome to engage in Part IV directly and to read it independently of the rest. From a talk I have recently given, I have discovered that the reader (or listener) may be all the more prepared to assimilate a given idea that the idea is truly revolutionary and radically new and that it has not the slightest resemblance or even the remotest relation with anything he or she may be familiar with. Of course, the idea has nevertheless to be consistent.

Perhaps I can introduce this idea along the following lines. I will start with a question. Imagine you are writing a foundational book on options (or on derivatives generally - let us not yet call them ‘contingent claims’), a script that begins from scratch, literally from genesis, as if you were writing the history of that world. Can you say what options are, what meaning they have, that is to say what difference they make, or what they are meant for, without using the notion of possibility or probability?

Imagine you are a speculative philosopher, and by this I mean that you wish to build your system of philosophy and your ontology from scratch, and that the notion of possibility is not available to you. Possibility and possible worlds are metaphysical constructs. As such, they don’t exist. Perhaps we will make them exist. Perhaps it will turn out we cannot talk of markets or of options without talking of possibility. Still, my question is for the moment: ‘Can we conceive of options, of their meaning and of their destination, without thinking of possibility?’

Options are contingent claims. The vanilla call option pays (S − K) if the stock price S is above the strike price K at the expiry of the option, and 0 otherwise. The formula ‘If . . . then, else if . . . then’ is the formula of contingency. It points to a dissymmetry in the otherwise indifferent space; it points to a difference. It also points to an event: something that can be, but that can be otherwise. This ‘making a difference’, or contingency, is the essence of options. This is the creative act of options, the productive difference they are made of.

Possibility has nothing to do with this. Contingency is of this world; possibility is of another world. There are even philosophers of the modern speculative brand (e.g. Quentin Meillassoux) who abhor metaphysics and the language of possibility and necessity as the totalization of possibilities, yet who believe that the world is only made of contingency and that the only necessity there is in the material world is the necessity of contingency. (I examine Meillassoux’s work at length in Part II.)

Possibility is only the metaphysical channel that we have invented in order to guide us to contingency. While contingency is all difference and shift and dislocation, possibility is but the (very understandable) move to fold that difference back on identity and on presence. The proposition of possibility is the following: Why don’t we imagine a process, a sequence of possibilities, that takes us to that contingency?

Possibility is a representation and, as such, it re-presents, it pins back on the presence of mind, the pure difference that contingency is supposed to make. Therefore, before I have even started talking about market completeness and the threat of redundancy of derivatives, you can tell that possibility, as a metaphysical notion, in itself already contains the germs of completeness or the death of the market. Possibility is already an attempt to bring back within the confines of representation, and to domesticate, the utter otherness of contingency.

In a world that is only made of contingency, it is only natural that we should invent options or derivative contracts. It is only natural that we should circulate, today, things that we know will make a difference in the future. This is why I have always thought of derivatives and derivatives markets as the technology of the future. Thus we write those derivatives contracts, and in their writing (the ‘If . . . then, else if . . . then’ formula) there is nothing even remotely related to possibility. It is the pure, material writing of contingency. It is pure difference. Writing is difference, as Derrida would say.

However, writing, as we all know and as Roland Barthes suggests, is only the prelude to an exchange.³ Typically, we write contracts when we are about to exchange something for fear that, when we no longer hold what we used to possess, in the interval of the exchange, but have let go of it in order that the counterparty may receive it, the counterparty might disappear, thus alienating us of our property.

Therefore, my next statement, as I am sure one can guess already, is that we write derivatives, those pure formulas of contingency, only insofar as we wish that the difference they will make in the future may make a difference today. Instead of wondering at their present value, we immediately go and see what difference they make in front of somebody else. This is the most direct statement that I could think of, to the effect that we write derivatives for the sole purpose that they may be exchanged and admit of a price. Price is a differential, not a splendid present value as general equilibrium theory holds. To price something is to trade something in order to earn a difference. It is to make a difference.

In the very essence of derivative writing, in its very meaning, the fact is embedded that they should admit of a price. The link is immanent and material. We don’t need possibility or metaphysics to travel from the derivative payoff to its present price. To be a derivative is to admit of a price. That is to say, to add a price, a new state of the market-world, to the existing prices.

Possibility and probability and stochastic processes, all these constructs, are themselves derivative concepts, that is to say secondary. They came later. Contingency and price (or market) came first. Market (both of the underlying asset and of any stratum of overlying derivative you care to write on it) is the original entity (note that ‘underlying’ will henceforth be used as a noun). Absent possibility and stochastic process, there is no way to talk of replication other than as static or intrinsic or model-independent. Creating a new derivative payoff - and by ‘new’ I mean that this payoff is not statically replicable with the existing ones - is only meaningful to the extent that it will bring to the table, i.e. to the market, a new price: that is to say a new ‘making a difference today’ by something that ‘will make a difference in the future in a new way’ (say an innovative, path-dependent or knock-out payoff).

It is fine that we should devise algorithms, as a matter of fact devise the whole metaphysical notion of possibility and probability, in order to compute present values of derivatives. I even think that tools that allow us to value and dynamically replicate derivatives are a constitutive part of the creation and growth of derivative markets (see chapter 3). However, given how I have straightened up the genesis of markets, going directly from contingency to price without the mediation of possibility, it should be clear that derivatives can have as their only meaning and destination that they may trade in a market and never end up perfectly replicable and redundant.

Therefore, when the Black-Scholes-Merton framework of option valuation - to only cite this paradigmatic case - shows that the option value is perfectly reducible to a number called volatility and to a deterministic replication strategy, this doesn’t mean the end of the game. On the contrary, this is just one way of slicing the price, and if this designates anything and puts pressure on anything, it designates that the thing called ‘volatility’ as the thing that you should expect, by virtue of the first principle that options must trade, to become stochastic.

Does this mean that the underlying process has changed and that you must now assume a process with stochastic volatility? No! Nothing has changed. The market is the eternally contingent and eternally self-differentiating thing it has always been; it is the single dice throw that you will never fit in a fully settled and developed representation of states of the world. It is your valuation tool that needs to change and evolve and differentiate⁴ - unless you combined your valuation tool with your trading skills and finally came up with the universal pricing tool that, hopefully, would never need changing, namely you the trader.

Part I

Writing and Event

1

Writer of The BLANK Swan

1.1 PREDICTION VERSUS PRESCRIPTION

1.1.1 My private Black Swan

Taleb has surprised me by giving me The Black Swan I expected most.⁵ For there to be a gift and a surprise, there must be a difference and an exchange. I couldn’t have given myself The Black Swan that I expected most (even though The Black Swan was, in a sense, already given to me, as I was acquainted with it and none of its themes came as a real surprise to me), for the reason that it takes two to make a gift and a giving, let alone an exchange. Not to mention that I couldn’t have personally written The Black Swan or even imagined that something like it could ever be written. What could there be to record, indeed, on the subject of the extremely improbable and of its impact, beyond the fact that the event goes down in history and records itself by itself when it occurs, all the deeper and the more indelibly that it was precisely improbable and had such a great impact?

I should thank Taleb for allowing this book - The Black Swan - ‘to write itself’, as he himself says in the prologue; it is only because The Black Swan is out now and because it is written that there could be material at all for my surprise. Recall that The Black Swan that I know best and am most acquainted with - the private The Black Swan I know so well that I could have written it myself - couldn’t possibly have surprised me in thought (not forgetting my intimate belief that it shouldn’t be written). In order to surprise me, it had to leave me and to differ from me; it had to leave my mind and assume the spaced and very different (almost strange) shape of the written material. In a way, our biggest surprise is when we come upon our own thoughts in a text that is not our own.

The literary work reverses the category of probability. True, a totally unexpected text may be thrilling, but what is more thrilling (and perhaps most thrilling) is that the material we are reading should fulfil us and correspond perfectly to what we want and what we expect - almost to the point of total coincidence - yet that the writing, this finite thread we are following word after word and spacing after spacing, should make it totally improbable and almost unimaginable, at every juncture, that such a thing should be written. This is why the greatest thinkers can make us the gift of the thoughts we expect most and understand best - our own thoughts - literally by writing them, by surprising us with the improbability, not of the thought but of the written text. This is why Wittgenstein is able to write, in the preface of the Tractatus, that only the reader who has had similar thoughts can understand his book.⁶ This is why he is able to write an impossible book, surprising us all the more that what was once impossible for thought becomes possible in writing, even necessary.⁷ This is why Pierre Menard is able to progress towards the only and, for this reason, most expected outcome of his writing process, Cervantes’ Quixote, without giving up the element of surprise and improbability at any point or any juncture.⁸

1.1.2 Pierre Menard’s trading room

Menard did not rewrite the Quixote, for then there would have been no risk in his enterprise. He truly wrote it. This tells us that there could be risk in writing without there being probability, or even possibility. From the point of view of possibilities, there is none facing Menard except to end up writing the Quixote, which is another way of saying that he faces no possibility at all.

I express this by saying that writing is a capacity, not a possibility. What Menard has done, in the process of his writing, is probe a space of variation of a new kind; he has hollowed out a trading room, strictly independent of the space of possible alternatives to the Quixote. Only in the writing of future, unknown texts is capacity confused with possibility, for the thought is then that the writer could have equally written another text. The tradability and the element of improbability in writing (what I have called the risk of writing) are then confused with the variability of the outcome within the space of alternative outcomes. In his endeavour of writing an existing text, Menard has managed, by contrast, to bring risk and probability apart again. Or rather, this is what Borges has managed to do, for Menard’s whole work and whole existence are, of course, totally incredible.

There is more to the space of trading/writing (I’ve called it a ‘room’) than just the collection of ‘preconceived’ alternative texts. Consider that Menard was absolutely equipped with the algorithm of perfect replication of the Quixote (since the Quixote already existed), yet he managed to trade it (I won’t say ‘to change it’, for he didn’t, or ‘to lose it then earn it back’, for he didn’t either - as I said, he just wrote it). The risk in trading/writing extends beyond probability. We can even define risk as that which sways and trades, after probability is done with and saturated. The market takes place - it starts - after the end of probability. It is the end that can start (the ‘can’ of capacity, not of possibility).⁹

1.1.3 Probability, replication, context and beyond

Probability is always defined relative to a given context or collection of states of the world.¹⁰ By replicating the derivative in all possible states of the world, the derivative pricing model exhausts probability and saturates the context. However, this is not yet trading. Trading the derivative is precisely what happens next. It puts into play the parameter (or parameters) whose fixity was the guarantee of fixity of the context and of the corresponding dynamic replication. For instance, option trading is a volatility play and volatility is assumed to be fixed by the replication algorithm of Black-Scholes-Merton.

Note that derivatives were written in order to trade (not in order to conceal payoffs in a sealed envelope that would be opened only at expiry). Derivatives are the natural offspring of the market and are the stuff the market is made of. (In a way, therefore, the market is also their produce: in fact, derivatives and the market are identical and not just hierarchically, or genetically, related.) Thus we see that trading (the process that is supposed to record a value, as of today and day after day, for the derivative that was once written and sentenced to have no value until a future date and unless a fraction of space) will never be the reiteration and the replication of the values that were initially planned for the derivative by the theoretical stochastic process and its prescribed dynamics.

The derivative valuation model is supposed to prescribe a value today, and every day, from the values the derivative is supposed to receive in the intervening states of the world, and in this it may seem indeed that the model is giving back to the derivative the present value it was once denied on account of its derivative nature and of the instruction to pay off in a future that may never be present and in a state of the world that may never be realized. The irony, however, is that this making-present of the deferred value of the derivative has no other present to be imprinted against but the present of the market and the actuality of trading. Derivative valuation models are intended for derivative trading and pricing, despite what all the academics working and theorizing in the field may have to say about that. Yet we saw that the trading of the derivative, or in other words its market, will by necessity take place and extend in this ‘improbable’ space we have called the trading room, and which is by definition absent from the replication plan and from probability.

I propose that risk, or the market, or contingency, is always posterior to context, possibility and probability. It always comes after probability, which is also a way of saying that context and probability are needed in the first place. Indeed, the market-maker wouldn’t be pricing the derivatives and trading them were it not for the derivative valuation model and the dynamic replication algorithm, which implicate him in the price process of the derivative.¹¹

Some have proposed that risk is all model risk. This is certainly compatible with my proposition and even derivative on it (where ‘derivative on’ means ‘derives from’; I will maintain this usage throughout the book, even though it may sound odd to the reader, because of the financial connotation of ‘being a derivative written on’.) However, I think this attitude is reductive of risk, in the last instance. It tends to put the model at centre stage and to depict risk only negatively and derivatively relative to the model. By contrast, my proposition of contingency exceeds the model and goes beyond it. It doesn’t counter the model but requires it. Contingency takes place after the model (as it takes place after the context and the probability), and for this reason it cannot limit itself to the model or be called ‘model risk’.

1.1.4 Contingency

Contingency is the writing/trading thread that we keep pursuing despite the fact that the context has been saturated by replication. Rather, the thread of derivative writing and trading (these two interchangeable sides of the destination of derivatives) is what the market is all about: the market as a writing process that is irreducible to a stochastic process; the market as a writing capacity, as a medium of contingency, that is irreducible to a writing possibility.

This is something I state of the market at large and not just of the derivatives market: what the market means in its essence. When you think of it, the story of the derivatives (which it would be more appropriate to call ‘contingent claims’, as we will definitely do, later) or equivalently the story of dynamic replication in Pierre Menard has only helped us separate the context from what exceeds it and helped us distinguish between possibility and contingency. It put this distinction in all the greater relief since it was necessary both to have the context and to trade through it (i.e. to change it) in order to ascertain the writing and the risk of writing, both of which are alternative definitions of the market. If, in some fancy world, the destination of the derivatives (i.e. their writing and its risk) hadn’t been bound up with the future and if it hadn’t been altogether meaningless to speak of the market except for the future, we could indeed have conceived of an extreme situation, like Pierre Menard’s, where the risk of writing had really nothing to do with possibility and everything to do with contingency.

The distinction between possibility, as always defined relative to a fixed context, and contingency, as the capacity of changing the context and of trading the text beyond its perfect replication, can be made more accurate by saying that this extraordinary writer, Pierre Menard, wasn’t facing just a single context or range of possibilities, one among which turned out to be the Quixote. A description like that would rather fit Cervantes, and this, by our reckoning, would imply that Cervantes did not in fact write the Quixote but created something that turned out to be the Quixote. It is interpreters, an extreme instance of whom is Pierre Menard, who face texts, not authors. Original authors face something else. For this reason, Borges’ novel can be considered an extreme meditation on interpretation.¹² What Menard was really facing is the Quixote as the one and only possibility (which is tantamount to saying he was facing a necessity), only his writing process was open to many, many different contexts.

1.1.5 The process of change of contexts

If we define ‘context’ as a range of possibilities and assume that different contexts may have some of their elements in common, then Borges has in fact described a strange individual who happened to worm his way inside a process without possibilities but with many contexts. This ‘worm process’ is, if you will, the set-theoretical intersection of all the contexts that admit the Quixote as one of their elements.

Now try to think what probability notion, if any, can be applied to a process like this. Later I will argue, as you might have guessed, that the market price process of derivatives, which is animated by ‘writers’ of the like of Menard who can trade and advance only insofar as they replicate the derivative that was once sealed and written, is such a process. It is a process of change of contexts (a.k.a. recalibration) not of possibilities. No probability can be applied to this process of change because probability can only choose among possibilities that fall within a single context.

Probability cannot be applied to Pierre Menard because the probability is equal to one, in each one of the contexts his writing process has traversed, to yield the Quixote exactly. For this reason, Menard cannot be said to pre-dict the Quixote. An adaptation of the word is needed to describe his forward-advancing enterprise, worming its way in a future without possibilities or in the pure medium of contingency (for there is no doubt that Menard faces his task as a future task and that it is risky). It is probably more suitable to say that Menard pre-scribes the Quixote.

Given the one and only possibility to which Menard has committed himself, what he is in fact trading is simply his own existence. This is always the case with writers who dedicate themselves to writing; however, Borges’ novel is specifically revealing in this respect in that it doesn’t even offer the writer the possibility of writing his own original text, for, otherwise, the choices and the sacrifices the writer would have to make would be confused with deliberations over the conception of the work and the future possible outcomes. What the fiction of Pierre Menard has achieved is to isolate the risk in writing that is in excess of the risk of thinking or, simply, of the risk of living the life of an original writer.

1.1.6 Writing the Black Swan

In my attempt at writing The Black Swan (or perhaps, as in Pierre Menard, at writing only the two chapters of the book that I desire most and that surprise me most), and for all the reasons that make its writing a necessity to me (for one thing, the fact that I already have its thoughts and cannot read it any more, and for another, that I really want to take the risk of writing it beyond possibility and probability, which means, by the same token, that I shall also be taking up the writing of risk - since it is the book of risk - and that I shall take that risk beyond probability), I shall then write it along the lines of the contexts, not along the lines of probability, and following contingency, not possibility.

I shall take advantage of the identity, already noted by the publisher, between what the book is about, the Black Swan, and what the book itself is, a Black Swan, to propose that the risk in my writing The Black Swan (the risk I shall be pursuing by changing and chaining together, in Menard-like writing style, the different contexts that lead exactly to The Black Swan - or, shall I say, to the Black Swan?) will be identical with the risk in The Black Swan (and by this I mean the topic of risk making up the content of Taleb’s book) and also, to some extent, with the risk inherent in the Black Swan as a pure, contingent event.

I shall also propose, as you might have already sensed, that the process of writing the Black Swan, that is to say the thread of writing/trading that takes place after the end of probability and the saturation of the context and qualifies, as such, as the medium of contingency, is the best way of predicting the Black Swan, or rather (given that the category of knowledge and probability are altogether dismissed at this stage) of prescribing it, and in this I would be strictly following the author when he declares, from inside the writing process of The Black Swan (and not from the outside point of view of somebody who expects probability in matters of risk and still thinks of the Black Swan in probabilistic terms), that The Black Swan wrote itself.

Only through the writing/trading performance, and not through the realizations of a theoretical stochastic process that is framed in representational thought, can the writer/trader of contingent claims exceed the saturated context and move to the next - i.e. he can trade. For this reason, my unoriginal and derivative writing/trading of The Black Swan will exactly consist in removing from the book all remnants of representation and probability and in arguing that the Black Swan is not a highly improbable event, as Taleb claims, but simply a case of change of context. It is a revision of the whole range of possibilities, not just of the probability distribution overlying them.

It is no wonder, then, that writing/trading should be adapted to the Black Swan, since writing /trading is precisely the process of context change and the medium of contingency. It is no wonder that the Black Swan should write itself and that we shouldn’t need somebody like Taleb to write about it, since contingency is another name for context change (or another name for the Black Swan) and writing is its medium (or another name for the process of context change).

1.1.7 Finding the context in The Black Swan

I shall remove the term ‘highly improbable’ from Taleb’s subtitle (and keep the indisputable ‘impact’) not only because his book is a certainty, even now a necessity, for my writing and no longer a remote possibility, but because this term, ‘highly improbable’, has had me puzzled from the start, in the light of what Taleb has to say about its impact. (Taleb has everything to say about the impact - note that the subtitle of the book, supposed to unpack the Black Swan for us, is The Impact of the Highly Improbable and not The Highly Improbable. Also, Taleb makes it very clear, in the first of his series of endnotes on page 311, that his problem is not about the possibility of a Black Swan but about the impact.¹³)

I feel puzzled because I can’t help wondering: Does the event carry impact because it is highly improbable (and this would be fair enough) or does the impact lie in the event being less improbable than we had thought (hence Taleb’s warning and whole message)?

From the start and as early as the subtitle, there is this unsettlement about the context in which Taleb wishes to frame the impact of the Black Swan. Which is why, in my writing of the Black Swan, I shall quickly move past and dismiss the two first attributes listed by Taleb: (1) that the Black Swan is an outlier and (2) that it carries an extreme impact, and find my true surprise in the last attribute (where Taleb’s gift to me truly lies), namely (3) that what characterizes the Black Swan (and, to my mind, characterizes it alone) is that we ‘concoct explanations for its occurrence after the fact, making it explainable and predictable’ (xviii).¹⁴

In my interpretation of the Black Swan, or rather in my writing of The Black Swan that is worth the risk of writing and even equal to it - and by this I mean that my writing shall proceed beyond probability to join the thread of change of contexts - I shall, therefore, change the context on Taleb and, instead of writing it from the point of view of probability, I shall write it from the point of view of context. I will argue that what is perceived by Taleb as a negative effect deserving only his irony, namely that the Black Swan should only be predicted - and the fitting narrative only produced - after the fact, will appear, from my point of view, as a plain, even a positive, effect of the Black Swan, for the mere reason that the Black Swan is a change of context and that it is only relative to a given context that we can make causal predictions at all.

To be fair, let me stress here that there is a continuous invitation in The Black Swan to look for the Black Swan outside the given context. Taleb talks of the domain-specificity of our reactions and a whole mode of thinking and of their dependence on the ‘context in which the matter is presented’ (53). He talks of ‘external uncertainty’ and of the ‘possibility of events straying from our mental projections’: the now well-known ‘unknown unknown’ (157). He specifically insists that ‘for an event to be a Black Swan, it does not just have to be rare, or just wild’ (improbability and impact are not enough) but that ‘it has to be unexpected, has to lie outside our tunnel of possibilities’ (213, my emphasis). As a matter of fact, he calls ‘Gray Swan’ the extreme event that lacks this last property and, consequently, he recognizes that a revision of our probability distributions or even of our whole framework of randomness, such as Mandelbrot’s fractals, even if it makes the extreme event less improbable, ‘does nothing to solve the Black Swan problem, but only mitigates it’ (262). What it manages to catch are just the Gray Swans, because something conceivable cannot be a Black Swan. (Here, finally, is the hint that the Black Swan is, above all, an inconceivable event.)

1.1.8 Writing backwards

In the light of all this, my writing over against Taleb can be seen as just an attempt at completing what he says, or rather at breaking with it completely by looking beyond probability and, as you will see later, beyond representational knowledge altogether. Perhaps it aims to solve the Black Swan problem or at least to establish the framework, both philosophical and technological, where it can be addressed. As the real Black Swan does not lie in the first two ‘conceivable’ or tractable attributes on Taleb’s list (the high improbability, the extreme impact - see Taleb’s discussion on hazard versus fortuit on page 272), this singles out the third, the backward narrative, as the decisive feature. Hence my writing can alternatively be seen as an attempt to establish the meaning, and the significance, of the backward narrative. This meaning is structurally linked to the context-breaching nature of the Black Swan.

Since the context ‘of’ the Black Swan is only available after it (and by ‘after it’ I mean ‘following it in chronological order’ and ‘following its style’), it is only normal that we should predict it after the fact. Once knowledge and probability have been dismissed as totally irrelevant to the process of writing/trading that I claim the market (as a species of history and medium of contingency) and even history (as contingency per se) are made of, it won’t in the least bother us that backward-looking narratives should be worth a try, even worth the risk, and even carry risk. (It remains to be said, of course, why we need them.) Recall Menard’s enterprise of predicting, or prescribing, an existing and totally past text. Recall that there was contingency and surprise (and in this sense, potentiality and room for trading) in Menard’s enterprise, and that this special brand of ‘future’ had nothing to do with knowledge or representation and everything to do with writing and performativity.

In Pierre Menard I have argued that the insertion in history and the event of appropriation (for Pierre Menard must have experimented, in his writing process, a series of appropriating events that really made the writing his own, and what’s even better, the writing of the Quixote!) were shown to be independent of the future (in the sense of ordinary, infinite, metaphysical time), for they just followed the thread of the writing of an existing text.

1.1.9 Poetry and The Black Swan

What Pierre Menard is doing is basically interpreting the Quixote (like a musical score) and this is why his task and his outlook are truly futural, even though, in his highly unusual case, Menard’s metaphysical future is reduced to the Quixote as only a possibility and his ‘narrative’ predicts only the past. Pierre Menard is not so much after the Quixote as he is after his own thread of appropriating events, in other words his own being. His existence and his whole work take place in a different ontological domain than the one in which the Quixote already exists or Taleb’s Black Swan readily takes place. A different sort of existential quantification (and qualification) should, therefore, apply to them.

Menard’s work is truly poetic. Its value doesn’t reside in its propositional content (for this is hopelessly equal to the Quixote) but in its poïetic drive. Poïesis means ‘to make’ in ancient Greek. The Wikipedia defines it as a word that ‘was first a verb, an action that transforms and continues the world. Neither technical production nor creation in the romantic sense, poïetic work reconciles thought with matter and time, and man with the world.’ ‘Whereas propositional language always addresses beings about which it speaks, poïetic saying brings being forth in the saying,’ writes Daniela Vallega-Neu.¹⁵ So it is not what Menard writes that matters, but how he writes it: the performativity of the writing, not its result. ‘Poetic moments are singular, non reproducible’, writes Richard Polt. ‘But this should not be confused with creativity or originality in the sense of mere novelty’. To illustrate the point, Polt then proceeds to cite exactly the case of Pierre Menard! ‘Each genuine appropriation is a unique event,’ he concludes, ‘even if it follows an established pattern, such as a musical score.’¹⁶

Similarly, the trader’s work is poetic. Since it is essentially of the future, it will always bring about novel possibilities, unlike Pierre Menard. However, what it brings forth - the trading room - is a performative capacity that is singular and nonreproducible to the extent that the trading individual is so much himself and that he has to be there in order that the market may be. Consider, by contrast, Taleb’s world, which seems to be given once and for all in its randomness and where the alphabet is just a device ‘to store information and reproduce it’ (30), where a narrative serves the only purpose of reducing dimensionality and where a novel, a story, a myth or a tale are all said to have the same function: to ‘spare us from the complexity of the world and shield us from its randomness’ (69-70)! Now consider again Menard’s work, in which the narrative doesn’t reduce anything at all, quite the contrary!

I am not sure that we write poems in order to reduce the dimensionality of the world or that we even set them against the ‘random background’ that Taleb wishes to recognize as only background and reality. But then, Taleb has not mentioned poetry in his list of narratives - intuition of an altogether different ontology, perhaps? (Poetry, especially by Hölderlin, was essential in Heidegger’s later thought of being as an event of appropriation.)

Saying ‘The king died, and then the queen died of grief’ instead of ‘The king died, and then the queen died’, is, to Taleb, an effective way of making us remember the two deaths. By adding information, it in fact reduces the dimension of history. Narrative is a human device and has no bearing on the real world, he says. I say: ‘What world?’ In mine, the narrative has in fact opened many dimensions, for I want to be that beloved king!

1.2 GENERALIZING PREDICTION

1.2.1 Postponing history

I will postpone until later the philosophical rift separating me from Taleb, namely that the question of our insertion in history (or in the market - for those among us who are absorbed in this peculiar subspecies of history) and of our dealing with its Black Swans is, to me, primarily a matter of ontology, even of the fundamental kind, whereas it is all epistemology to him, perhaps even naturalized. In a typical moment, Taleb writes: ‘I know that history is going to be dominated by an improbable event, I just don’t know what that event will be’ (154). I wonder whether this is typical Taleb or typical Yogi Berra. The way to insufflate substance in this statement is to say that this is simply how history happens and what history is. Simply define history as the series of Black Swans and drop the ‘I know’ and the ‘I don’t know’. Ontology, instead of epistemology. What’s more, the ‘is’ of your ‘history is’ will not be empty. It is blank, because it has to be filled by writing.

I will postpone until later my major disagreement with Taleb, namely that the question of history (or of the market) is too great and too overwhelming a phenomenon not to claim us completely and require our writing as the only site out of which it can be posed. It is too great, in any case, to fall under Taleb’s hasty metaphysical reductionism and to be identified with a mere output that would be available to his inspection, as if from outside. (Taleb speaks of ‘the script that produces events’ or of ‘the generator of history’ (8). He speaks of the ‘generator of the world’ (268), of the ‘generator of reality’ (270), of the ‘model which runs the world’ (267) and, in other places, of ‘that big machine that generates events’ (12). Even truths are ‘generated by mechanisms’, according to him (20). ‘The true explanation is unique’, he writes, ‘whether or not it is within our reach’ (72).)

For now, I will content myself with what is, to my eyes, the biggest surprise of The Black Swan (Taleb’s true gift to me) and that is the realization that, if the Black Swan is indeed understood as a context-changing event, then it is truly mine: I have already covered it; I have already written it!¹⁷

1.2.2 Incompatible contexts

It is in Taleb’s chapter on the ludic fallacy that I was struck by the illumination that the Black Swan is, in fact, a non-probability-bearing event of change of context or, in other words, a truly contingent event. Of the three different sources of Black Swans that Taleb describes in his book: (1) the Black Swan that is inherent in our genes and in our evolutionary blindness to extreme events (I have always disliked naturalized epistemology), (2) the Black Swan, or rather the Gray Swan, that is the result of mistaking the Gaussian probability distribution of Mediocristan for what should be, ‘in reality’, the scalable laws of Extremistan (I will come to that below) and (3) the Black Swan that cannot possibly be predicted because it falls beyond knowledge and probability (that is to say, it falls beyond the given range of possibility), I retain the third as the philosophical one (therefore worthy of my attention). The other two are either merely anthropological or disappointingly metaphysical.

Taleb cites the example of a casino in Las Vegas whose real risks turned out to be incommensurate with what could be anticipated, knowing that the business was a casino (129). ‘The four largest losses incurred or narrowly avoided by the casino’, he notes, ‘fell completely outside their sophisticated models.’ They were triggered by (1) the loss of an irreplaceable performer in their main show after he was maimed by a tiger he considered to be his partner, (2) the attempt to dynamite the casino by a disgruntled contractor, (3) a tax violation, almost causing the casino to lose its gambling license, and (4) the kidnapping of the casino owner’s daughter, causing him to dip into the casino coffers to secure the ransom. These Black Swans, Taleb observes, ‘swamp the on-model risks by a factor of close to 1,000 to 1’.

In my opinion, these Black Swans are not, technically speaking, outliers. They simply are not part of the universe of possibilities initially envisaged by the casino. Each belongs to a different context, utterly foreign to gambling. Taleb himself recognizes that they initially belonged outside the casino’s building. Sure enough, the casino’s management will from now on provision for losses that might be triggered by kidnapping, by tax negligence, by dynamite or by a tiger’s appetite, and by this I mean that the corresponding state of the world, exotic as it may be, will be added to the existing list of states of the world. However, the key notion here is the incompatibility of contexts prior to the experiment, not the enumeration of utterly heterogeneous objects and items, which is always a possibility after the fact or may be, at best, the projection of a playful and erudite imagination.

Borges (yes, him again) is known for his capacity (yes, capacity) of producing improbable enumerations, the most famous of which occurs in The Aleph. His ‘Chinese encyclopaedia’ has fascinated many a thinker and Michel Foucault opens The Order of Things with a dip into it.¹⁸ Taleb must have had in mind incommensurable enumerations of this sort when he spoke of the narrative as a means of reducing their dimensionality (71), and he typically cites Borges at this juncture (‘Funes, the Memorious’). As a matter of fact, Borges’ style must have altogether interpenetrated Taleb’s as his short novel Yevgenia’s Black Swan definitely resonates with Borgesian tones to my ear.

Two contexts are said to be incompatible when they cannot be fused together and are not commutative. What this means is that the results of an experiment involving them can massively differ depending on the order in which you bring the two contexts to bear. Had the casino ‘experimented’ with the context of dynamite or tigers (and I mean the whole context, not the isolated fact that was just their outcome) before experimenting with the context of casinos, chances are it would have taken up the business of demolition contracting or wild animal breeding instead of gambling, possibly with a jackpot machine inserted in one corner of the cafeteria for the entertainment of employees and visitors.

Compare the turkey example, also cited by Taleb (40). The story goes like this. After a thousand days of feeding, confidence in a bright future is at its highest in the turkey’s mind, until something unexpected happens on the Wednesday before Thanksgiving. My observation is that the context of feeding the turkey and that of wringing its neck are not so incompatible. It is all a matter of food, after all! Taleb can rightly talk of a sudden revision of belief, in the turkey’s case, instead of a complete change of context, because the wringing of the neck definitely belongs to the turkey’s context, only the turkey stupidly assigns to it zero probability. For all practical (and epistemological) purposes, it is indeed as if it wasn’t there. However, the turkey could have believed otherwise and, as a matter of fact, Taleb examines the alternative shrewd turkey which would consider the feeding as a confirmation of the danger of being turned into supper (188).

Incompatibility of contexts, by contrast, invalidates such counterfactual reasoning. It is a much more severe predicament, because it is impossible to even begin to group the possibilities belonging to the two contexts in the same universe of possibilities, and this is irrespective of the probabilities they would get. For instance, Taleb need not lament our ingratitude towards the invisible hero of 9/11 who manages to avoid the disaster by imposing continuously locked bullet-proof doors in every cockpit on September 10, 2001 (xxiii) because this thought experiment is counterfactually invalid. States of the world after 9/11 are incompatible with states of the world before, and avoiding 9/11 or the zero probability that the disaster gets in Taleb’s heroic scenario is simply not defined because it cannot exist before its own context, which is 9/11. ‘Hero’ - like all the names that history dispenses - seems to be a hopelessly contextual notion.

When contexts are commutative they can be subsumed under a larger context, which is simply their set-theoretical union, and both the experiment and the language reporting it can be set against this global context. In this way, language can forget about the context and how it may affect the facts of the experiment or its objects and speak of the objects and their revealed properties as if they were independent of the context and