The Blank Swan: The End of Probability

October 19th 1987 was a day of huge change for the global finance industry. On this day the stock market crashed, the Nobel Prize winning Black-Scholes formula failed and volatility smiles were born, and on this day Elie Ayache began his career, on the trading floor of the French Futures and Options Exchange. Experts everywhere sought to find a model for this event, and ways to simulate it in order to avoid a recurrence in the future, but the one thing that struck Elie that day was the belief that what actually happened on 19th October 1987 is simply non reproducible outside 19th October 1987 - you cannot reduce it to a chain of causes and effects, or even to a random generator, that can then be reproduced or represented in a theoretical framework. The Blank Swan is Elie's highly original treatise on the financial markets – presenting a totally revolutionary rethinking of derivative pricing and technology. It is not a diatribe against Nassim Taleb's The Black Swan, but criticises the whole background or framework of predictable and unpredictable events – white and black swans alike – , i.e. the very category of prediction. In this revolutionary book, Elie redefines the components of the technology needed to price and trade derivatives. Most importantly, and drawing on a long tradition of philosophy of the event from Henri Bergson to Gilles Deleuze, to Alain Badiou, and on a recent brand of philosophy of contingency, embodied by the speculative materialism of Quentin Meillassoux, Elie redefines the market itself against the common perceptions of orthodox financial theory, general equilibrium theory and the sociology of finance. This book will change the way that we think about derivatives and approach the market. If anything, derivatives should be renamed contingent claims, where contingency is now absolute and no longer derivative, and the market is just its medium. The book also establishes the missing link between quantitative modelling (no longer dependent on probability theory but on a novel brand of mathematics which Elie calls the mathematics of price) and the reality of the market.

Table of Contents:
Introduction xv Part I Writing and Event 1 1 Writer of The BLANK Swan 3 1.1 Prediction versus Prescription 3 1.1.1 My private Black Swan 3 1.1.2 Pierre Menard’s trading room 4 1.1.3 Probability, replication, context and beyond 4 1.1.4 Contingency 5 1.1.5 The process of change of contexts 6 1.1.6 Writing the Black Swan 7 1.1.7 Finding the context in The Black Swan 8 1.1.8 Writing backwards 9 1.1.9 Poetry and The Black Swan 10 1.2 Generalizing Prediction 11 1.2.1 Postponing history 11 1.2.2 Incompatible contexts 11 1.2.3 Knowledge as prediction 13 1.2.4 True empiricism 14 1.2.5 Meta-contextual prediction and backward causality 15 1.3 The Derivatives Market 18 1.3.1 Possibility, capacity and the market of contingent claims 18 1.3.2 Market mechanics 19 1.3.3 Price and the implicate ontology 19 1.3.4 Technology of the future 21 1.3.5 Context change and the necessity of jumps 23 1.3.6 The ‘derivative–derivative’ trader 24 1.3.7 Bringing the Black Swan to nest 25 1.3.8 The regime-switching model as a meta-contextual pricing tool 26 1.3.9 ‘Transcendental deduction’ of the derivatives market 27 1.3.10 A return to history 28 2 The Writing of Derivatives 31 2.1 First Steps on the Surface 31 2.1.1 Theoretical speculation versus speculation 32 2.1.2 Rethinking probability 33 2.1.3 Nonarbitrage 34 2.1.4 Writing, difference and deferral 37 2.1.5 Reality of the market: the virtual 38 2.2 Introducing Contingency 40 2.2.1 Derivative writing as an alternative to metaphysics 40 2.2.2 Inverting the logic 41 2.2.3 Present value versus present price 42 2.2.4 Derivative technology 43 2.2.5 From derivatives to contingent claims 45 2.2.6 The medium of contingency 46 2.2.7 Possibility versus capacity 47 2.2.8 Immanent differentiation and univocal contingency 49 2.3 The Pricing Surface 51 2.3.1 Reversibility of pricing and absolute market 51 2.3.2 Price and exchange 54 2.3.3 The two faces of price and reversion to the surface 55 2.3.4 The liquidity and the fold of price 56 2.3.5 The new metaphysics of liquidity and of the past of prices 58 3 The Event of the Market 61 3.1 From States of the World to Market Prices 61 3.1.1 The market, a place of exchange not of prediction 61 3.1.2 Value versus price 63 3.1.3 Elements of financial valuation theory 63 3.1.4 The advent of derivatives and market prices as states of the world 64 3.2 The Black–Scholes–Merton Paradigm 65 3.2.1 Price process and Brownian motion 65 3.2.2 The Black–Scholes revolution and derivative pricing theory 66 3.2.3 The dynamic replication of derivative instruments 67 3.2.4 A universal pricing formula 68 3.3 The Critique of Derivative Pricing Theory 70 3.3.1 The real consequences of derivative pricing theory 70 3.3.2 The very special mode of being of the market 71 3.3.3 The market as given 72 3.3.4 The market as the ‘inversion’ of theory or the ambivalence of price 73 3.4 The Necessity of Meta-Contextual Ascent 75 3.4.1 A new ‘logic’ for a new science 75 3.4.2 New generations, endless generation 77 3.4.3 The necessity of the context and the necessity of its surpassing 77 3.4.4 A meta-contextual pricing tool 79 3.4.5 Technology of the future versus knowledge of the future 82 3.4.6 The performative surpassing of representation and possibility 83 4 Writing and the Market 87 4.1 Pierre Menard 87 4.1.1 The reality of contingency 87 4.1.2 The im-possibility of history 89 4.1.3 Writing history 91 4.1.4 The very sad writing of Pierre Menard 92 4.1.5 The differential definition of writing and the unpredictability of the Quixote 95 4.1.6 The past of possibility 97 4.2 Reading and Writing 100 4.2.1 The significance of replication and the turn to the virtual 100 4.2.2 Writing as forgetting 103 4.2.3 Anti-memory as trading and literary creation 104 4.2.4 The resurfacing of writing 107 4.3 Approaching the Market 108 4.3.1 Univocity of the market 108 4.3.2 Immanence of the market 111 4.3.3 The sense of the market 113 4.3.4 Announcing the genesis of the market 115 4.3.5 Originality of price and of the market 116 4.3.6 The Blank Swan 118 Part II Absolute Contingency and the Return of Speculation 123 5 The Necessity of Contingency 125 5.1 Against Speculation 125 5.1.1 Writing history (reprise) 125 5.1.2 The writer’s (and trader’s) body 126 5.1.3 Beyond possibility, capacity and ethics: a political interlude 128 5.1.4 State of power 129 5.1.5 The absolute 131 5.1.6 Absolute irony 132 5.2 Speculative Materialism 132 5.2.1 Speculative metaphysics 132 5.2.2 The shortcoming of Kant’s critical philosophy 133 5.2.3 Meillassoux’s proposition: the absolute necessity of contingency 134 5.2.4 Is the absolute thinkable? 136 5.2.5 The absolutization of facticity 137 5.2.6 Positively thinking the absolute 138 5.2.7 Chaos, yet not without structure 139 6 Passage to the Future 143 6.1 From Possibility to Inexistence 143 6.1.1 The passing of the possible 144 6.1.2 Factual ontology 145 6.1.3 Cantor’s set theory as meta-ontology 146 6.1.4 Factual derivation of the un-totalization 147 6.1.5 Effective contingency versus absolute contingency 148 6.1.6 Speculative result versus metaphysical result 149 6.2 The Passage 150 6.2.1 The future and the world 150 6.2.2 Passage to the future 151 6.2.3 Gravity of the world 152 6.2.4 The quality of happening 153 6.2.5 Turning the future on 155 6.3 The Future 156 6.3.1 Badiou and Deleuze 156 6.3.2 Ontologizing the passage 157 6.3.3 Cutting to the future 158 6.3.4 A paper rotation 159 6.3.5 Keeping only the future 160 7 Necessity of the Future 163 7.1 A Model World 163 7.1.1 Derivatives world 163 7.1.2 The event of trading the derivative 164 7.1.3 Exchange as fundamental ontology 166 7.1.4 The market as the exchange of knowledge 167 7.1.5 The market as the process of history 168 7.1.6 Arche-exchange 168 7.2 The Implied Absolute 169 7.2.1 The absolute is in the inversion 169 7.2.2 Why derivative pricing is not a human science 171 7.2.3 The implied volatility smile is the absolute truth 173 7.2.4 Implication is faster than thought 174 7.2.5 The market as the last absolute 175 8 Necessity of Writing 177 8.1 Radical Speculation 177 8.1.1 Elevating implication 177 8.1.2 The ‘What?’ question 178 8.1.3 Thinking speculation reflexively 178 8.1.4 Critical speculation 179 8.1.5 Absolute speculation 181 8.1.6 Implication as the radicalization of speculation 182 8.2 The Pricing Alternative 183 8.2.1 Price as a crossing 183 8.2.2 The absolutization of mathematics 183 8.2.3 The mathematics of price 184 8.2.4 Price as the exchange of metaphysics and possibility 186 8.2.5 The ‘letter’ of the necessity of contingency 187 8.2.6 Immanence and materiality of price 188 8.3 From the Market to Work 189 8.3.1 Price is the other of thought 189 8.3.2 Meillassoux’s body 190 8.3.3 The work (of the trader, of the poet) 191 8.3.4 Writing the world 192 Part III Flight to Sydney, Or the Genesis of the Book 195 9 The Mathematics of Price 197 9.1 The Absolute without Thought 197 9.1.1 Mathematical thinkability 197 9.1.2 The absolute without necessity 199 9.1.3 Impossible exchange 201 9.1.4 Writing as nonmetaphysical speculation 203 9.2 The Absolute within Thought 205 9.2.1 Philosophy of the event 205 9.2.2 Necessity as tension 208 9.2.3 The event of thought 209 9.2.4 Deep necessity versus superficial speculation 211 9.2.5 The cohesion of thought 212 10 Barton Fink 217 10.1 The Pledge 217 10.1.1 Passivity of thought and the exchange surface 217 10.1.2 Fiction, fabrication and dynamic programming 219 10.1.3 The first mark on the surface 221 10.1.4 The partition 222 10.2 The Turn 224 10.2.1 The turn of the world 224 10.2.2 The violence in movie-making 225 10.2.3 The probability distribution 228 10.2.4 Partition of the world and shoe distribution 229 10.2.5 The bellhop 232 10.2.6 Time frame and deadline 233 10.2.7 Woman, or the end of the partition 234 10.2.8 The sum total of possibilities and the problem in the head office 235 11 The Narrative Adventure 237 11.1 The Line of Flight 237 11.1.1 The other end of the world 237 11.1.2 The book of derivatives 238 11.1.3 Tour du monde versus point of the world 239 11.1.4 Flight to Sydney, or the retro-adventure 241 11.2 The POINT of the World 243 11.2.1 Flight to the virtual 243 11.2.2 Eternal turn versus eternal return 246 11.2.3 Writing after the departure of possibility 247 11.2.4 The narrative from the point of the world 249 11.2.5 The Australian bank, book and market 250 12 Out of the Box 253 12.1 The Purple Gastropod 253 12.1.1 Quants and the enterprise-wide system 253 12.1.2 Integration versus differentiation 254 12.1.3 How to be Australian 255 12.1.4 Creators of a boîte 257 12.1.5 After dinner 259 12.2 The Point of Return, the Point of Inversion 261 12.2.1 The mark, the market and the point of return of the world 261 12.2.2 Turning the world into a point, inverting the surface 263 12.2.3 Blindness and insight 264 12.2.4 Inverting the world, and the only remaining question 265 12.2.5 From theory to the narrative adventure, to the only remaining book 268 12.3 How to be a Writer 269 12.3.1 My place as a writer 269 12.3.2 My memory of the market 272 12.3.3 Walking on my head 276 12.3.4 Double writer, double trajectory 279 13 The Prestige 283 13.1 Finding the Market, Binding the Book 283 13.1.1 Reversibility between the book and the market 283 13.1.2 Sydney process and writing process 286 13.1.3 Marketing the philosophy book, and my trademark 287 13.1.4 The infinite duration of writing 288 13.1.5 The question of the book, the equation of the book 291 13.2 Absolute Deterritorialization 293 13.2.1 Making the point of the market 293 13.2.2 Head office and blank box 298 13.2.3 The revolutionary and virtual exotic market 300 13.2.4 How the plane of immanence takes precedence 303 14 The Geographical Process 305 14.1 The Field of Ruins 305 14.1.1 Ancient Greece, the market and Australia 305 14.1.2 The market as field of ruins and geographical process 306 14.1.3 The method of the intuition of the market 308 14.1.4 The becoming of the book and the pressing of the ruins 310 14.1.5 The dwelling of the virtual and the implosion of the ruins 313 14.1.6 The book after the market and the cross of history 314 14.1.7 Pulling out the tool, drawing the book and withdrawing in a hotel 318 14.2 Landing on the Market 320 14.2.1 The tool to write the market 320 14.2.2 Reality of the market 325 14.2.3 Absolute exchange 327 14.2.4 Exchange as a category of its own 329 14.2.5 Option volatility smile and exchange 332 14.2.6 The heart of the market 336 Part IV Conversion of Credit into Equity, Or the Genesis of the Market 341 15 History of the Market 343 15.1 The Conversion 343 15.1.1 The significance of the convertible bond 343 15.1.2 Genesis of the market 343 15.1.3 Passivity and activity 344 15.1.4 The moment of the conversion 345 15.2 Possibility versus Contingency 347 15.2.1 Contingent claim versus projected possibility 347 15.2.2 Pricing versus evaluation 347 15.2.3 Price and the stochastic process 348 15.2.4 The meaning of the market and the volatility smile 351 15.2.5 Possibility unmasked and return to the virtual 353 15.2.6 Backward possibility 354 15.3 The Market 357 15.3.1 The privilege of the market 357 15.3.2 The place of the trader 358 15.3.3 The trader as a writer of last resort 360 15.3.4 The end of the flight in possibility 361 15.3.5 Summary 362 16 From Debt to Equity 365 16.1 Deduction of the Contingent Claim 365 16.1.1 Debt, death and contingency 365 16.1.2 The morphing of debt into equity 366 16.1.3 The conversion/conservation of writing 367 16.1.4 Company of the future 368 16.2 Deduction of the Exchange 370 16.2.1 The past of debt and the definition of probability 370 16.2.2 The exchange place as the conversion of face 371 16.2.3 Breaking the circle of representation 372 16.2.4 The market without possibility 373 16.2.5 The market as the medium of contingency 375 16.2.6 The impossible exchange 376 16.3 Deduction of Price 379 16.3.1 Price as the ‘value’ of the contingent claim 379 16.3.2 How does price differentiate? 381 16.3.3 The atemporal pit of price 382 17 The Market and the Philosophy of Difference 385 17.1 The Pit of Price 385 17.1.1 The price of exotics as the key 385 17.1.2 Price as intensive difference 386 17.1.3 Price as meaning 388 17.1.4 Price and the intensive conception of time 390 17.2 The Market and Time 392 17.2.1 The market as noncausal redistribution of probability distributions 392 17.2.2 Creative time 395 17.2.3 Creation as eternal return 397 17.2.4 The single dice-throw 398 17.3 The Market and Difference 403 17.3.1 The pure order of time 403 17.3.2 Internal difference 405 17.3.3 The market as philosophy and conversion as meta-philosophy 406 17.3.4 Immanence and the ontology of multiplicities 409 17.3.5 Reawakening the virtual 411 18 Future of the Market 415 18.1 The Category of Price 415 18.1.1 Price as interface 415 18.1.2 Possibility as a pretext for writing 418 18.1.3 The past of possibility 420 18.1.4 The aleatory point lying at the heart of the contingent claim and the exchange 421 18.1.5 The market, as exchange, is the answer to the impossible exchange 424 18.1.6 Time-to-expiry versus place 426 18.2 The Step Beyond 427 18.2.1 Reactivating the conversion 427 18.2.2 Possibility is only a tool 429 18.2.3 The pricing tool 432 18.2.4 Making money in the market 433 18.2.5 The market as alternative to probability 435 18.2.6 Suppressing possibility 436 18.2.7 Thinking of contingency instead 437 18.2.8 Beyond the financial market 439 18.3 Place and Contingency 440 18.3.1 The sense of place 440 18.3.2 The power of price 442 18.3.3 A life in contingency 443 18.3.4 Success and succession 445 18.3.5 Becoming the market 446 18.4 Conclusion 448 19 Appendix 1 The Logic and Mathematics of Regime Switching 449 A1.1 Description of the Regime-Switching Model 450 A1.1.1 Regimes 450 A1.1.2 Risk-free yield curve 451 A1.1.3 Dividends 451 A1.1.4 Regime probability 452 A1.2 General Backward Equations 452 A1.2.1 Stand-alone default regime 453 A1.2.2 Coupled nondefault regimes 453 A1.2.3 Fixed dividends 454 A1.2.4 Proportional dividends 454 A1.2.5 Vanilla calls 454 A1.3 Credit Default Swaps 454 A1.3.1 Definitions 454 A1.3.2 Value in default 455 A1.3.3 Backward equation 455 A1.4 Calibration 456 A1.5 Recalibration 456 20 Appendix 2 From ‘Being and Time’ to ‘Being and Place’ with Jeff Malpas 459 Bibliography 463 Index 467

About the Author :
Elie Ayache was born in Lebanon in 1966. Trained as an engineer at l'École Polytechnique of Paris, he pursued a career of option market-maker on the floor of MATIF (1987-1990) and LIFFE (1990-1995). He then turned to the philosophy of probability (DEA at la Sorbonne) and to derivative pricing, and co-founded ITO 33, a financial software company, in 1999. Today, ITO 33 is the leading specialist in the pricing of convertible bonds, in the equity-to-credit problem, and more generally, in the calibration and recalibration of volatility surfaces. Elie has published many articles in the philosophy of contingent claims, as well as a book, dedicated to the philosophy of writing.