Expanding on my summary of Ray Brassier’s Remarks on Subtractive Ontology and Thinking Capital here are some further related observations on aleatory rationalism, drawing on Elie Ayache’s account of how the option ‘science’ of the derivatives trading comes to hypostasize the market as an absolute relation that is not thought-independent:
Brassier’s critique of aleatory rationality shares the epistemological concerns of Quinten Meillassoux, who at the end of his philosophically innovative work After Finitude attempts to offer a speculative resolution to Hume’s problem of induction; questioning the traditional ludic understanding of randomness and how certain varieties of intractable uncertainty impinge upon us in the form of large-impact rare events. Ludic fallacy finds its apotheosis in the financial markets, particularly in derivatives trading; something that French theorist Elie Ayache has noted leading him draw upon Meillassoux to better explain how the misapprehension of traders affects the dynamic meta-stability of the real with false certainties. Ayache is an ex-volatility trader, working at a time when physical scientists such as engineers were co-opted by the markets in order to work on option science, providing workable algorithims for market traders wishing to price options contracts. Options trading requires the pricing of options on underlying assets in order to create futures contracts, locking a ‘strike price’ – in what is known as put-call parity – to be realized at a later date (i.e maturity). These derivatives are financial instruments which are derived from the underlying price of another asset (an index, event, value or condition), all of which are reliant on the unpredictability of volatile markets or more accurately, we could say it is a process of speculation on speculation. Ayache draws upon and deepens Nassim Taleb’s highly influential – if somewhat one-sided – explanation for the current global economic crisis. Taleb’s Black Swan hypothesis falls within the ambit of Hume’s problem of induction, which casts doubt on inferential reason.
The Black Swan event refers to the catastrophic failure in 1987 of the Black-Scholes-Merton model for deriving future prices from underlying assets and ultimately attempts to replicate risk-free portfolios by damping stochastic turbulence [BS, p.3]. Black-Scholes is a differential equation reliant on large data-sets of market performance and is imported from physics as a way of predicting trends in stochastic conditions – the Brownian motion of prices. Both Taleb and Ayache claim the failure Black-Scholes to be a completely unforeseeable and gratuitously random event; a probabilistic aberration. Up until then Black-Scholes had been satisfactory model of realization. The model’s dramatic failure in 1987 was the single counter-instance of the model’s falsification and thereafter it was used in reverse in order to continue to derive value. Both authors question the model’s overall empirical fitness due to its reliance on the assumption of market completeness. Furthermore, following in the footsteps of Badiou, Ayache places an emphasis on the event that makes it ‘impossible to prescribe [as] a process of history’ [FTS1, p20]. It is also here that Badiou’s unbinding of the figure of history in the face of the void as possibility of possibilities is combined with Meillassoux’s diagnosis of the problematic nature of the correlation between thought and being. Ayache, with regard to the problematic inscription of the event within processural history, states that:
‘[...] the impossibility of prescribing a process for history is no ordinary impossibility in the sense of lack of possibility. The impossibility of processing history is incommensurable with possibility because the “process” of history is a change and shift and disruption of whole ranges of possibilities. A more accurate characterization would be to say that the “process” of history is an im-possible process.” [FTS1, p.20]
He then stipulates that whilst we can traditionally read world history as a ‘process of possibilities’, there is a special class of possibilities that don’t occur in possibility, but in capacity. By capacity he means the active ‘writing of history’, ‘price process’ or ‘market process’ that materially writes or translates to produce something original and unprecedented. For him, writing is the voluminous space of decision – he equates the writer with the stock-trader, the one who physically interjects himself subjectively into an stochastically unverifiable space created by dynamic replication – over which he ‘imposes his own necessity’ [FTS1, p.21] in order to behave independently and originally. This forcing allows him to progress beyond the im-possibility of prediction and mere empty replication of the same. If the writing process is held as equivalent to the price process, this has complex implications when applied to the concrete case of derivative markets: ‘The pricing/trading of a derivative is this inscribed in capacity not possibility, for it amounts to changing the context and changing the range of variables’ [FTS1, p.22] For Ayache, price as market given (datum) ‘resurfaces from possibility’ in what appears to be a transition from pricing ability to pricing capacity (i.e. from possibility to writing). Here we can detect a movement from unverifiable volatility to computable pricing, that subsequently determines marketable hedging options. Ayache is adamant this requires the physical interjection of the trader’s body to allow the pricing process of the derivative to resurface ‘from the depths of possibility’ and rejoin the pricing surface, emerging as ‘process history’, which in turn generates new contexts and variable parameters. This appears, at least superficially, to bear all the hallmarks of Badiou’s aleatory rationalism; the Mallarméan throw of the dice, the moment in which the trader plucks price from supernumerary excess. It is in this the moment in which the derivatives seller (writer) is exposed to the real, the moment he forces a subjective prediction in the face of the storm of hyperChaos.
This exposure to what Brassier refers to as stochastic noise and Meillassoux calls the transfinite – the ‘detotalization of number‘ [AF, p. 103] – is precisely why this part of the trade cannot automated, since it is non-axiomatizable and beyond the limits of calculatory reason. Operations within a space that is incompossible specifically require the subjective intervention of a human trader. Indeed, market prediction cannot be fully automated, since it would demand computers to be armed with perfect information, but this level of completeness and compression is exactly that which is precluded by Turing’s halting problem and Chaitin’s halting probability; it is common knowledge that the term market forecast is merely a figure of speech. And whereas machines execute algorithmic models in the market, it requires humans to interpret the feedback to modify the model. Therefore, it is through the creation of trader’s own necessity in the face of unverifiable that they produce a computable price from the excessive possibility of possibilites (or more specifically given-without-giveness). When traders write derivatives they are creating a pure formula of contingency, wishing that the difference they will make in the future may make a difference today, given that price is a differential. In so doing, the writer obscures underlying value with price, proliferating informational opacity and undermining empirical claims with regard to any market models. As Ayache states: ‘Traders do not trade derivatives indifferently.’ [FTS2, p.47] This allows Ayache to ask: ‘Isn’t the market the perfect embodiment of the co-relational circle?’ [FTS2, p.47], since no fixed mathematical law can provide an empirically given price for the market and absolutization occurs precisely when the market model is reversed. This is the instance in which the market is confused for reality, denoting a certain circularity that leads us to question the limits of deductive reasoning and ‘science’ of rational expectation. Here we could say that the market itself is hypostasized as an absolute relation that is not thought-independent. Here the market becomes a opaque rendering of the world wherein we can only maintain the ‘fact’ of the market and not the in-itself. This absolutization implies that crisis in the market is a crisis in faith, borne out by repeated need for sellers to ‘fudge’ (or modify) the Black-Scholes-Merton model in order to render it functional. The competitive advantage pursued by those who engineer the sophisticated complexity of derivatives – layered speculation and the interpenetration of models – comes at a cost to transparency, which in turn drives leveraging and the securitization of products of unknown and uncertain value. Moreover, there is a proliferation in variations of the model, precisely in order to create opacity and informational asymmetry in order to protect profit margins. This antithesis of parity in finance is characterized by opaque markets, black-box trading and dark pools of liquidity that escapes any State regulation or taxation of these unobserved flows of capital; an estimated one-third of all trading exceeds any such legislation.
Ayache E. (2008) The French Theory of Speculation Part I: Necessity of Contingency (Wilmott Magazine) pp. 20- 29.
Ayache E. (2008) The French Theory of Speculation Part I: Necessity of the Future (Wilmott Magazine) pp. 44-49
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