![]()
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 couldnât 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 couldnât 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 - âto write itselfâ, 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 - couldnât possibly have surprised me in thought (not forgetting my intimate belief that it shouldnât 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, Cervantesâ Quixote, without giving up the element of surprise and improbability at any point or any juncture.8
1.1.2 Pierre Menardâs 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 Menardâs whole work and whole existence are, of course, totally incredible.
There is more to the space of trading/writing (Iâve called it a âroomâ) than just the collection of âpreconceivedâ 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 wonât say âto change itâ, for he didnât, or âto lose it then earn it backâ, for he didnât 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 âcanâ 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 âimprobableâ 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 wouldnât 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 âderivative onâ means âderives fromâ; I will maintain this usage throughout the book, even though it may sound odd to the reader, because of the financial connotation of âbeing a derivative written onâ.) 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 doesnât 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 âmodel riskâ.
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 âcontingent claimsâ, 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) hadnât been bound up with the future and if it hadnât been altogether meaningless to speak of the market except for the future, we could indeed have conceived of an extreme situation, like Pierre Menardâs, 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, wasnât 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, Borgesâ 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 âcontextâ 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 âworm processâ 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 âwritersâ 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, Borgesâ novel is specifically revealing in this respect in that it doesnât 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 Talebâs 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 ca...
