What is price? It is ‘cost of something bought or sold, something sacrificed to get something else, sufficient bribe, measure of value of something,’ says Encarta . ‘Price’ is most often given by the amount of money an item or service would bring if or when it is sold, defines ‘ Accounting, Business Studies and Economics Dictionary ’ (www.tuition.com.hk). “I know my price, I am worth no worse a place,” says Iago in Othello . “Our rash faults make trivial price of serious things we have, not knowing them until we know their grave,” rues the king in the Bard’s All’s Well That Ends Well .
Now, sample this: Price is ‘the present trace of future contingency (the present signal) without the line of communication of possibility (which presupposes the actualisation of metrical time).’ The line of communication that price uses is the conductive medium of the market, and the market is conductive of contingency, says Elie Ayache in ‘ The Blank Swan: The end of probability ’ (www.wiley.com).
Sounds philosophical? Brace up for more. The market-maker doesn’t need time and possibility, and his activity of pricing the contingent claims (in their entire range and in all the variety of their payoff structures) is demonstrably contradictory with possibility, notes the author. “All he needs, as he follows the string of prices of the underlying and of the contingent claims, is to remain afloat on the surface of the market: to make money. And so he will, but not by possibility.”
Contingent claims transmitted
The market is not a generator of prices unfolding in time, but the atemporal medium that is conductive of contingent claims and that transmits them as prices, Ayache explains. And the elementary (molecular) property of the market-medium that makes it conductive of contingent claims in the form of prices is the exchange, he adds.
The exchange, to him, is the place we have no choice but to let go of the contingent claim, by valuing it. “Only this won’t be value in the sense of convergence towards face. We don’t face the contingent claim the way we face debt: the way we stare at redemption or contemplate the abyss. Precisely, we can let go of the contingent claim because we are not inexorably pulled towards its face.”
The 1987 crisis
With that perspective, the author looks back at the events of October 1987 – when ‘the options market crashed, the Nobel Prize winning Black-Scholes formula failed and volatility smiles were born’ – and says it was an exchange crisis. In 2008, however, the crisis went back to the creation of price and not just to its event, he feels.
“1987 was a good crisis in the sense that it hit a population already equipped with the means to surmount it. It hit options traders who were immersed in the market, actively engaging in dynamic replication, already testing the limit of the whole category of possibility on which their pricing tool was based.”
The traders quickly relearned the meaning of the conversion and the genesis of the contingent claim by inverting their formula, recounts Ayache. “They gave back to contingency its precedence, no longer pricing the contingent claim from the automatic and impassive replication strategy formulated only in possibility, but started now implying volatility from the market price of the contingent claim in order to compute the replication strategy, as this was the only way they could reaffirm their position as dynamic traders, despite the apparent abuse and misuse of the model that this meant, literally.”
From identity to differentiation
Conversion, as the author elaborates, is not just the transformation of debt into equity; more generally, it is the conversion of the principle of identity and convergence inherent in debt and possibility into the principle of differentiation inherent in the contingent claim. “Its morphological or topological expression is the conversion of the face/ abyss of debt into the cut/cross of the contingent claim, or the conversion of the time-to-expiry of debt (or, equivalently, of the backward procedure of evaluation in possibility) into the open place, the exchange place where the ex-partner of the debt, formerly detached in the no-place of his bond, now becomes an active trader.”
Ayache observes that a conversion crisis occurs every time this eternal return to place (which is the face of contingency) is forgotten and replaced by the space of possibility and its fixed states of the world. He avers that a crisis occurs every time the process of differentiation of price, which needs possibility only as a tool, only to the extent that it shall constantly depart from it and vary from it, thus truly weaving its fabric, is supplanted by a possibility that no longer differentiates and that remains identical.
Correlation, the big culprit
The 2008 crisis is not even technically a credit crisis, says the author. He reasons that credit derivatives such as CDS (credit default swap) would never have posed a problem had they not been bundled in CDOs (collateralised debt obligations), whose valuation then crucially depended on the correlation between individual defaults.
Cautioning that default correlation is a probabilistic object that is notoriously difficult to model, let alone to hedge or to infer from the market, Ayache declares correlation as the big culprit. He argues that the true crisis – the one where the conversion of the principle of identity into the principle of differentiation was forgotten – is the consequence of having based the valuation of the most complex of derivatives, the so-called correlation products, on possibility and not on contingency, on a pure probabilistic model and not on the market.
How to make money?
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 ,’ the intro states. Ayache rues that the real intellectual scandal faced by the whole ‘culture’ of the market today is that traditional 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.”
For an immersive study, on a solitary afternoon, with the inevitability of meditative consequences.
