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.
Preface Introduction 0.1 Derivative Valuation Theory vs. Derivative Pricing Technology 0.2 Implied Volatility vs. Real Volatility 0.3 Formal Reality vs. Physical Reality I The Matter 1 The End of Probability 1.1 The Void of Possibilities 1.2 A New Matter 1.3 The Infinity of Markets 1.4 The End of Statistics 2 The Vision Ahead 2.1 Regime-Switching Model 2.2 Recalibration 2.3 Is Probability Necessary? 2.4 Price and Probability 2.5 A New Metaphysics 2.6 Absolute Contingency 2.7 The Market as an Opportunity for Speculative Thought 2.8 The Market as the Conversion of the Image of Thought 2.9 Ascending to the Metalogical Level 3 Introducing the Market 3.1 The Unexchangeable Place of Exchange 3.1.1 The market as a continual event 3.1.2 The market as quantitative history 3.1.3 The intensive nontemporal price process 3.1.4 The continuity of the discontinuity 3.1.5 The matter beyond antifragility 3.2 The Medium of Contingency 3.2.1 The technology of the future 3.2.2 The book behind the market 3.3 Pricing vs. Valuation 3.3.1 The surface of the market 3.3.2 The smile problem 3.3.3 The absolute local 3.3.4 In the middle of the event 4 The Thought Behind 4.1 Two Sides of Writing 4.2 Genesis of Price vs. Generation of Number 4.3 The Market as Geometry 4.4 State vs. Mark 4.5 Probability as an Internal Episode 4.6 The Alternative Axiomatic System of Shafer and Vovk 4.7 Extensive Difference vs. Intensive Difference II The Matter in Brownian Motion 5 From Throwing the Dice to Grasping Brownian Motion 5.1 The Meaning of Probability 5.1.1 The Law of Large Numbers 5.1.2 Intuition 5.1.3 Matter 5.1.4 Reality 5.1.5 Tense 5.2 Changing the Meaning of Matter 5.2.1 Money 5.2.2 Time is not money 5.2.3 Money is place 5.3 Changing the Meaning of Reality 5.3.1 Ex-ante vs. ex-post 5.3.2 Brownian motion 6 From the Marvel of Brownian Motion to the Reality of the Market 6.1 The Technology of the Market 6.2 The Reality of the Market 6.3 The Market as an Inverted Order of Thought III The Matter in Contingency 7 The Paper and the Tree 7.1 The Market and Time 7.1.1 Contingency, writing and exchanging 7.1.2 Price and time 7.1.3 Price and the event 7.1.4 Price and the trace 7.2 From the Mark to the Whole Market 7.2.1 Contingent payoff vs. contingent claim (first take) 7.2.2 The invention of writing (first take) 7.2.3 The exchange and the abyss 8 Archaeology of the Multiple 8.1 To Be vs. Can Be 8.1.1 Identification and transition 8.1.2 The danger of abstraction and the suspension of possibility 8.1.3 0 and 1 8.1.4 The real future 8.2 Chrono-logic 8.2.1 Probability as an integral 8.2.2 Chronology as a simulation of chrono-logic 8.3 Accounting for the Event 8.3.1 Money and the other face of the event 8.3.2 The accident of time and the necessity of work 8.3.3 An event that is not but that remains 8.3.4 Writing the event 9 Archaeology of the Exchange 9.1 All of the Market! 9.1.1 Impossible exchange, necessary exchange 9.1.2 The inverse view 9.2 Statistics as a Proto-market 9.2.1 Abstraction and the precision of the present state 9.2.2 The immanence of statistics and the immanence of the paper 9.2.3 The matter in statistics 9.3 The Matter in the Exchange 9.3.1 The non-individual singular 9.3.2 Single-case statistics 9.3.3 Contingency of the strike 10 Matter and Geometry 10.1 The Singularity of Writing 10.2 The Singularity of the Exchange IV The Market of Contingent Claims (or the Matter in Black- Scholes-Merton) 11 Towards a Contemporary Theory of the Market 11.1 The Stochastic Narrative of the Market 11.1.1 Definite states 11.1.2 Derivatives prices as states 11.1.3 Variations on lottery value and random price 11.1.4 The curse of the derivative value 11.2 The Trading Narrative of the Market 11.2.1 Can the derivative trade independently? 12 Incomplete Markets 12.1 Complete vs. Incomplete Markets 12.2 Martingale Measure of the Market 12.3 Equivocation 12.4 Incomplete Market when the market Is All There Is 13 The Central Knot 13.1 Contingent Payoff vs. Contingent Claim 13.2 Probabilistic Exit 13.3 The Alternative Exit 13.3.1 Differentiating the form 13.4 The Invention of Writing 13.5 Genesis 13.5.1 That they don't exist 14 The Hard Problem 14.1 The Ultimate Probability Spot 14.2 The Presentation of the Contingent Payoffs 14.3 The Lure of Theory 14.4 The Semantic Theory of the Market 15 The Book of the Market 15.1 Formalism and Meta-formalism 15.1.1 The instant of the formalism and the instant of the market 15.1.2 The infinity of the option price and the infinity of matter 15.1.3 Formal deduction of matter 15.1.4 A new book for a new reality 15.2 The Book of Genesis 15.2.1 Only the book can write history 15.2.2 One book instead of two theories 15.2.3 Only the book can bind the void 15.2.4 Only the book can settle the succession 15.2.5 Contemporary art 15.2.6 An ontology made of paper 15.3 The Trading Force 15.4 Coda 16 Denouement: The theory after the Two Narratives Conclusion 17 Appendix 1: Regime-Switching Model 669 17.1 A Meta-contextual Pricing Tool 17.2 Recalibration 18 Append
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