Video Description
A Talk from Annual Conference 2024
We consider thought under its two indissociable aspects, concept and intuition. You can only expand the concept by analysis, and fail to synthesize objects, in Kant’s sense of objects of possible experience. For that purpose, something must be added to the concept, which is sensibility, or intuition. Concepts without intuition are empty, according to Kant.
Probability theory is a theory of the concrete world, as such indissociable from possible experience. For this reason, there is something more in probability theory than in real analysis. It is the concrete situation, or trial of the world, or random sample ω, without which probability theory would lack the two characteristic notions of independence and repetition. The trial ω is the Kantian sensibility or intuition of probability theory. The event A, which alone is subject to analysis and is assigned probability, thus admits the concrete situation ω as content ( ω ϵ A).
Under the concepts of probability theory, the Black-Scholes-Merton (BSM) analysis leads only to the dynamic replication of contingent payoffs, and to no market thereof. To change constant volatility into stochastic volatility does not help. In order to exist, the derivatives market requires a new form of Kantian sensibility, or intuition, or concrete situation, which we denote by ϖ. The situation ϖ of the market is radically different from the situation ω of probability theory or statistical analysis. Implied volatility is logically (even temporally) incompatible with historical volatility.
The specific sensibility of the market , ϖ, is the “exchange”. As Helyette Geman says: “BSM is risky by definition because it amounts to exchanging volatility.” As a result, BSM must be thought differently. It becomes the first instance of the “market models”, whose conceptual analysis relies on the “trading decision” and the “pricing function”, or the very denial of probability and stochastic structure.
Speaker Bio
Elie Ayache
Elie Ayache is a former option market-maker on MATIF (1987-1990) and LIFFE (1990-1995). He is the co-founder (1999) and currently the CEO of ITO 33, a software company specializing in convertible bond pricing, and more generally equity index and equity-to-credit single name derivative pricing. Elie is the author of The Blank Swan: The End of Probability (Wiley 2010) and The Medium of Contingency: An Inverse View of the Market (Palgrave 2015).