In The Medium of Contingency Elie Ayache builds upon his ground-breaking book The Blank Swan, in exploring the intersection of philosophy and finance, introducing new notions of price and market. Inverting the received view, he now sees a creation of matter in both the market and its metaphysics, rather than pure speculation.

Once recognized as the proper medium of contingency and disassociated from the probabilistic and statistical tools traditionally used to model it, the market can be thought as 'real', in a new sense of reality corresponding to the new sense of matter. To bring this new and original perspective, The Medium of Contingency builds on probability theory as first formalized by von Mises and Kolmogorov, and later revisited by Shafer and Vovk. It utilises the author's extensive experience in derivatives pricing technology and software, as well as his work in the philosophy of contingency and contingent claims, to propose a new philosophical interpretation of Brownian motion and of the Black-Scholes-Merton formula. Then it completes the overturning of the traditional view of the market by arguing that there should be no difference, ultimately, between an underlying asset and the derivative written on it.

This book does not aim to change the market but the way we must think of it. It is the author's conviction that there can be no philosophy of the market, and consequently no thinking of it, without a philosophy of contingent claims and of derivative pricing. The book provides the missing piece, which the philosophy of probability cannot provide alone. Its scope, however, extends beyond the strict critique of financial mathematics, as it also, and perhaps most importantly, delivers the author's definitive treatment of the philosophically prominent and recently much discussed notion of contingency.

possibility, but as a direct medium of contingency from which possibility was withdrawn, or as the material technology of the future from which knowledge and prevision have been withdrawn. In this transformation, thought, we might say, has been brought from the depth (or the illusion of depth5 ) to the surface, from abstraction to matter, from thought to writing. And the market has become necessary, not through the summation or totalization of possibilities, but through the subtraction and

embrace the aporia according to which yet another book will be written and, no matter what we think, it is still the book. One has to understand this wholeness of the book (the whole book, the whole market) as a homogeneous medium whose acceptance amounts to repeating the event and no longer being separated from it (or, which to amounts to the same, accepting the single stroke). Thought has had a tendency to grasp the real against a fixed frame (of thought) that keeps thought separated from the

the derivative value as being the output of his formula or the product of his replication strategy but, rather, consider the derivative market price as the reason to recalibrate the formula. If the only way of getting the instantaneous volatility that is needed in the BSM formula is by implying it from the given option market price, then this by itself implies that the BSM formula is soon to be recalibrated and the implied volatility soon to change when it is inferred from the next option price.

the meaning of probability – and meanings are real, albeit not empirically verified – is that the frequency will precisely converge to that number in the infinite long run, in an appropriately repeated experiment. To be more exact, the strong law of large numbers is a mathematical proof in Kolmogorov’s formalism, and is therefore unquestionable; however, in order for it to connect with reality, and for probability to acquire its objective and precise meaning, it is necessary (a) to interpret the

essential and formal, when the goal is to establish a theory of probability. We say of a certain die that it has a certain probability of producing a certain outcome, as if probability was inherent in the die. Some would argue that the inherence of the probability in the die is a definitive and acquired property that must be conceived independently of its subsequent manifestation in the statistics of outcomes. Probability may not be an exact finite physical science in the sense that probabilistic