Fundamental Articles

Fundamental Articles

IMPLIED PROBABILITY OF BAIL-IN

May 2020

An immediate, fundamental change in thinking is required to take the panic out of the Contingent Convertible/AT1 Bond market, Philippe Henrotte tells Wilmott.

VALUING CONVERTIBLE BONDS WITH 20-OF-30 SOFT CALL PROVISION

June 2015

Farhad Firouzi, quantitative analyst, and Elie Ayache, co-founder and chief executive officer of ITO33, present a fast and accurate method of evaluating one of the most daunting features of the convertible bond market - convertible bonds with the soft call feature of 20 out of 30 days.

WHICH MODEL FOR EQUITY DERIVATIVES?

March 2012

Local volatility was, for a long time, seen as being a universal panacea. However, cracks appeared and we have been forced to look elsewhere for a new framework.

DIVINING DIVIDENDS

August 2011

A convertible bond holder is short dividend. When a dividend is paid, the underlying share drops by a fraction of this dividend.

DIAL 33 FOR YOUR LOCAL CLEANER

December 2006

““Elie Ayache pulls off the philosopher’s mask and reveals himself to be the … well, I won’t spoil the surprise. What our good friend Ayache does do, I can reveal, is take on implied volatility just one last time in an epic article worthy of a good stiff drink and absolute silence…” (Paul Wilmott, from the Ed’s Letter).”

HOW EXOTIC IS THE VARIANCE SWAP?

October 2006

The local volatility model helped give birth to a liquid equity variance swap market. But, Philippe Henrotte writes, the ungrateful child has now matured and is about to terminate its creator …

THE IRONY IN THE VARIANCE SWAPS

August 2006

Learn how Irony always supersedes Theory in derivative pricing, according to Elie Ayache.

THE EQUITY-TO-CREDIT PARADIGM

August 2006

Elie Ayache traces how convertible bond pricing went from a specialist niche to a new paradigm in volatility arbitrage.

BUCKETS IN THE HOLD OF THE TITANIC

February 2006

““Out-of-model risk results from the empirical recognition that no model is immune to internally inconsistent re-calibration,” Philippe Henrotte writes.”

WHAT IS IMPLIED BY IMPLIED VOLATILITY?

December 2005

““Implied Volatility is not just a word or a concept,” Elie Ayache writes.”

SUPER CALIBRATE STOCHASTIC EXOTIC OPTION ANALYSIS!

March 2005

Calibration, recalibration and co-calibration. These, according to ITO33, are the keys to unlocking the problem of derivative pricing.

CAN ANYONE SOLVE THE SMILE PROBLEM? A POST-SCRIPTUM

December 2004

A return to issues raised by an article published in January last year.

THE EQUITY-TO-CREDIT PROBLEM (OR THE STORY OF CALIBRATION, CO-CALIBRATION AND RE-CALIBRATION)

January 2004

Elie Ayache explains why the regime-switching model answers the challenges of re-calibration and co-calibration in the equity-to-credit problem.

UNIVERSAL INTERFACE GENERATOR

January 2004

Vadim Zeitlin explains why it may be interesting to provide the users of C++ pricing libraries with the possibility to call them from any language of their choice.

THE CASE FOR TIME HOMOGENEITY

January 2004

““Departure from time homogeneity may be the sign of serious modelling deficiency,” writes Philippe Henrotte. With three important examples, Philippe shows that it is possible to calibrate parsimonious time homogeneous models to complex term structures. His examples include the volatility smile, the credit spread, and the yield curve.”

CAN ANYONE SOLVE THE SMILE PROBLEM

January 2004

Elie Ayache, Philippe Henrotte, Sonia Nassar and Xuewen Wang address the problem of smile dynamics and how it can be solved.

PRICING CROSS-CURRENCY CONVERTIBLE BONDS WITH PDE

January 2004

In a finite element framework, Nabil Ouachani and Yunzhi Zhang analyze the pricing of cross-currency convertible bonds where the underlying share is denominated in a currency foreign to the convertible bond issue.

NO FEAR OF JUMPS

January 2004

Yann d’Halluin and David Pooley propose robust and efficient techniques for the numerical solution of option pricing models where the underlying process is a jump diffusion process.

ACCURATE EARLY EXERCISE FREE BOUNDARIES FOR AMERICAN PUTS

January 2004

Toufic Abboud and Yunzhi Zhang present a numerical method for computing the free boundary problem for the American Put.

NEXT GENERATION MODELS FOR CONVERTIBLE BONDS WITH CREDIT RISK

October 2002

Elie Ayache, Peter Forsyth and Ken Vetzal examine the impact of default and of several recovery assumptions on the pricing of convertible bonds in reduced-form credit risk models.

GOD'S MODEL VS. MARKET MODELS PART III: MAN'S MODEL

January 2022

We recognize in Black– Scholes–Merton the ‘model of a carpenter’, and we seek ways how truthfully to generalize it.

GOD'S MODEL VS. MARKET MODELS PART II: THE IMPORTANCE OF A BOOK

November 2021

Two fundamental concepts of Bergomi’s, the trading decision and the pricing function, turn probability merely into an interpretation.

GOD'S MODEL VS. MARKET MODELS

September 2021

A thorough reading of Bergomi sheds new perspectives on rough volatility in relation to the meaning of the options market.

A TRUTHFUL GENERALIZATION OF BLACK-SCHOLES-MERTON

January 2021

Black-Scholes-Merton was never equipped to face an options market. The formula doesn’t know what an options market is and even less so what the meaning of inverting the formula and implying volatility from the option market price could possibly be.

TIME AND BLACK-SCHOLES-MERTON

April 2017

No statistics can represent the abyss of the event. Only the market can, provided the story is told right.

FROM WITHIN

March 2017

What is the smile problem? How can it be interpreted? Do people really understand it?

THE MEDIUM OF CONTINGENCY

May 2016

Dan Tudball discusses the consequences of inverting our thinking about the market with Elie Ayache.

ACTUARIAL VALUE VS. FINANCIAL PRICE

October 2011

Financial pricing, in its usage of the term ‘real probability’, has not managed to unshackle itself completely from actuarial valuation. Even though the market of contingent claims is the long-awaited technology that would finally allow us to account for the future contingent events without using probability…

PLOTTING THE GRIM REAPER'S PATH

March 2011

Plotting the grim reaper’s path

SINGLE-CASE STATISTICS?

February 2011

The myth of ex-ante valuation.

THE END OF PROBABILITY

October 2010

Not only does the market not need probability, the market replaces probability.

THE TURNING

June 2010

And now for something completely different …

THE BLANK SWAN

April 2010

Dan Tudball talks to Elie Ayache.

I AM A CREATOR!

June 2008

Elie Ayache explains why you must always think outside the box, yet keep the box with you at all times.

I AM A FRENCH SPECULATOR!

April 2008

The capacity of writing provides the missing link between the Kerviel case and the credit meltdown argues Elie Ayache.

THE FRENCH THEORY OF SPECULATION, PART II

February 2008

‘Necessity of the Future. Elie Ayache: From the Hume-event to the 1987-event, through Cantor and Badiou.’

THE FRENCH THEORY OF SPECULATION, PART I

December 2007

Necessity of Contingency. As a fresh (and French) theorist of speculation, Elie Ayache combines a French president and a young French philosopher.

HOW NOT TO BID THE MARKET GOODBYE

October 2007

Credit led to the “disappearance” of the market; Elie Ayache ponders how we should make preparations for its return.

AUTHOR OF THE BLACK SWAN, PART II

August 2007

The best way to predict the Black Swan is to write it, claims Elie Ayache. In other words, to replicate it, to trade it, to exchange it. This is why his Black Swan is set against Taleb’s, and in a way, written all over (against) it.

AUTHOR OF THE BLACK SWAN, PART I

June 2007

The best way to predict the Black Swan is to write it, claims Elie Ayache. In other words, to replicate it, to trade it, to exchange it. This is why his Black Swan is set against Taleb’s, and in a way, written all over (against) it.

THE NEXT QUESTION CONCERNING TECHNOLOGY, PART II

April 2007

Elie Ayache contends that dynamic replication is the “inaugural event” of derivatives markets. Ayache continues his theme and shows how the October 1987 crash can be seen as the “other” beginning of derivatives markets. Both beginnings (the first and the other) are required in order to address the question of the next technology for derivatives markets.

THE NEXT QUESTION CONCERNING TECHNOLOGY, PART I

February 2007

Elie Ayache contends that dynamic replication is the “inaugural event” of derivatives markets. Ayache continues his theme and shows how the October 1987 crash can be seen as the “other” beginning of derivatives markets. Both beginnings (the first and the other) are required in order to address the question of the next technology for derivatives markets.

WHY 13 CAN ONLY SUCCEED TO 11, OR, THE END OF PROBABILITY

June 2006

Learn how Capacity, not Possibility or Probability, is the dynamic trader’s main virtue, according to Elie Ayache, and how derivatives markets are the technology of the future.

THE "NON-GREEK" NON-FOUNDATION OF DERIVATIVE PRICING

August 2005

Learn how the philosophy of Jacques Derrida can provide the “non-foundation” of the founding paradox of derivative pricing, according to Elie Ayache.

BEING AND THE MARKET, PART II

June 2005

Elie Ayache proposes that the market is a new “epoch” of Being.

BEING AND THE MARKET, PART I

April 2005

Elie Ayache proposes that the market is a new “epoch” of Being.

PROBABILITY AS THE OTHER FACE OF KNOWLEDGE

February 2005

Uncovering a broader view of probability by taking a lead from Quantitative Finance.

THE BACK OF BEYOND

October 2004

Elie Ayache takes a step beyond essential uncertainty to tie up a few loose ends.

A BEGINNING, IN THE END

August 2004

The concluding part of the discussion on a new view on quantitative finance.

A NEW PHILOSOPHY FOR A NEW SCIENCE

June 2004

Introducing a new voice in option language and the central question all quants need to ask.

DEFINITIVE SMILE MODEL, PART II

May 2004

““Why should we write about smile models?” asks Elie Ayache. “This is the question behind the question. For if the definitive smile model is not yet in sight, perhaps a definitive smile story is possible.””

DEFINITIVE SMILE MODEL, PART I

April 2004

““Why should we write about smile models?” asks Elie Ayache. “This is the question behind the question. For if the definitive smile model is not yet in sight, perhaps a definitive smile story is possible.””

OPSCORE WEB SERVICE

November 2017

ITO33’s Opscore Web Service delivers easy, cutting-edge engagement with the convertible bonds market for non-specialists.

NEXT FINANCE

February 2008

‘Elie Ayache : “Le trading des produits dérivés n’a rien à voir avec les distributions de probabilité” Il fut un des premiers traders de volatilité sur le matif ! Fondateur d’ITO33 et ancien responsable de la recherche à Dexia AM, Elie Ayache nous livre sa réflexion sur les Marchés dérivés qu’il définit comme la technologie du futur…’

ASIAN CONVERTIBLE BONDS - AN OPTION ON OPTIONS

September 2007

We speak to Elie Ayache at ITO33, who dissects various layers of complexity in Asian Convertible Bonds and ASCOT and sheds light on their popularity.

OUR MOST EXOTIC PRODUCT

November 2005

Learn how this strongly path-dependent asset is alive and kicking at ITO33.

ONE STEP BEYOND

December 2003

Elie Ayache discusses his forthcoming regular column with Dan Tudball exploring the need for a philisophical foundation in quantative finance.

THE BLANK SWAN

The Blank Swan is available for purchase on Amazon, Google, Barnes and Noble and Wiley, among others.

THE BLANK SWAN - The End of Probability

By Elie Ayache

This book is packed with philosophy and if you don’t handle it with care it will explode in your hands. If you open it properly, however, you will find an explosion of meaning in every sentence and every word and a constant challenge for thought. Some say its writing style is difficult, which is true, no doubt. I am not here, indeed, to cajole the reader, and least of all, to condescend to vulgarize my topic.

Throughout its writing, I was guided solely by the thought of the market – a thought, as you will all agree, that is compelled to diverge and to constantly break out, lest the sequence converges and the market comes to a halt. I haven’t been interested by the domains but by their limits, and beyond their limits, by inverting the domains. I have travelled the logic of derivative pricing to its end, tracing this journey in my book, and found no final passage to the market but in inverting the traditional order of thought and in placing price before probability and absolute contingency before possibility. The result is a reconstruction of the market of contingent claims in the realm of writing and difference instead of identity and delimitation of states.

Both in the philosophical argument and in the writing strategy, I have avoided every naivety in thought and every comforting station, finding the disappearance of the market as the last contingency that it is necessary to think, especially in these days. This is the moment when the book, as a binder, and the market, as a domain, can no longer contain thought and when their non naive recovery requires a total revolution. One in which the metaphysics of the market becomes the market as metaphysics and the interior of the book becomes the world inverted.

Elie Ayache

“I am relieved to finally find a book that deals with Black Swan Events in a new way. Ayache brings a reverse-probabilistic perspective … so, view this as a gutsy look at the ’end of probability’ and how we will need to envision the world once we get rid of this artificial, antiquated tool. I am also glad to see that those of us trained in the trading of options can have views original enough to influence the philosophy of probability and the philosophical understanding of contingency.”

Nassim Nicholas Taleb, author of The Black Swan

TIME AND BLACK-SCHOLES-MERTON

50 years have passed since the advent of this incredible model, and our contention, on its 50th birthday, is that time must be completely reinterpreted. Time in the BSM formalism has nothing to do with time in the BSM trading practice, according to us. Damiano Brigo has shown, for instance, that two underlying dynamics can exhibit the same historical volatility (computed on a fixed discrete time grid) yet imply totally different options prices, or totally different implied volatilities. This, he has shown in the formalism, or in formal time, where the notion of historical volatility exists indifferently in the past or in the future. We claim that in material time, or in the time of the market and actual trading, the situation is even worse and the notions of historical and implied volatility are even more separate. Simply, historical volatility can only exist in the past, and implied volatility is the only thing that exists in the future.

GOD'S MODEL VS. MARKET MODELS

Recent propositions in derivative pricing and stochastic volatility modelling suggest that truth exists below the surface of derivative and asset prices, truth as seen from God’s point of view. Technically, it is the ‘rough volatility model’. They call it ‘God’s model’. By contrast, the ‘Market models’ approach finds no place for such underlying truth, or indeed underlying stochastic process, and believes only in surface models, where derivatives are themselves the underliers and their price is the only fact, produced solely by the machinic, automatic, autonomous and anonymous logic of the market.

DON QUIXOTE ON WALL STREET

In this talk – perhaps the most significant we’ve ever engaged with – and after saying how unpardonable the omissions and additions perpetrated by Bachelier, we will show that the future should really be written and not merely predicted; equivalently, that the pricing function of the market models is forward-looking, and not backward-looking like the usual statistical models underlying it. We hope this is not, as Borges would put it, “one of those parasitic works which situate Christ on a boulevard, Hamlet on La Cannebière, or don Quixote on Wall Street.” Indeed, we think the final term of a theological or metaphysical proof is no more final, no more uncommon, than ours. The sole difference is that philosophers publish the intermediate stages of their work, while we are resolved (for now) to suppress those stages of our own.

NEITHER GOD NOR MACHINE: MAN'S MODEL

Recent propositions in derivative pricing and stochastic volatility modelling suggest that truth exists below the surface of derivative and asset prices, truth as seen from God’s point of view, and that this final truth is the rough volatility model. By contrast, the market models approach (e.g. Bergomi) finds no place for such underlying truth, or indeed underlying stochastic process, and believes only in surface models, where derivatives are themselves the underliers and their price is the only fact, produced solely by the machinic, automatic, autonomous and anonymous logic of the market.

We attempt to strike the right balance between these two extremes, and to find the only truthful derivative pricing model, neither God’s nor the machine’s: what we call Man’s model.

A TRUTHFUL GENERALIZATION OF BLACK SCHOLES MERTON

When truly scrutinized, the Black-Scholes-Merton model and formalism have no notion of an options or generally derivatives market. The only market is that of the underlying asset and all that the formalism shows is how to synthesize payoffs that depend on the underlying stock price. These are internal to the underlying market and hardly qualify as independently exchangeable assets. Consequently, the only true problem facing BSM is how to move from volatility to implied volatility (i.e. how to admit the existence of an options market) and not how to move from constant volatility to stochastic volatility. Elie will claim that this simple and deep observation, and the corresponding redirection of thought, lead to the regime-switching model as the only truthful generalization of BSM.

GLOBAL ART FORUM 2018: I MAKE PRICE

‘I Make Price’, Global Art Forum, Singapore 2018: Talk and conversation with Shumon Basar (video courtesy of ArtScience Museum)

DE L'ABSTRACTION REELLE DE LA MONNAIE AU CONCRET ABSOLU DU MARCHE FINANCIER

Élie Ayache
Colloque Alfred Sohn-Rethel
Nancy, Décembre 2018

COLLOQUE DES ACTUAIRES 2018

“Instabilités stabilisées”
La volatilité stochastique : Le modèle, de la description à l’action
Elie Ayache
Colloque de l’Institut des Actuaires
Paris, Décembre 2018

WRITING AND PRICE

From abstract probability theory to pricing technology.

QUALITATIVE VOLATILITY

Two deductions of price from the concept of pre-quantitative volatility. Talk at New School, New York.

WRITING THE FUTURE

Talk at the Royal Academy Schools. Why the future must be written, not predicted: the case of Pierre Ménard and the market of contingent claims.

THE NECESSARY BOOK IS SUBTRACTED FROM CHANCE

Talk and book launch event of ‘The Medium of Contingency’ at the Sursock Museum in Beirut. The author, Elie Ayache, in conversation with Philippe Henrotte and Gerald Nestler. Where contingent books, necessary books and impossible books are discussed, as well as their relation to the market of contingent claims.

ELIE AYACHE ON SPECULATION

Elie Ayache on speculation, both financial and metaphysical.

THE FUTURE WAS THE MARKET

A ‘contingent claim’ is another term for a financial derivative with a payout dependent on the realization of some future contingent event. In turn, the future prices of these contingent claims become new future events on which further contingent claims are written. When ‘The Market’ is defined as this endless material chain, argued Elie Ayache, time drops out of the equation and the future, literally, is no longer ahead.

Elie Ayache

PROBABILITY TREE VS. CONTINGENT CLAIM

Elie Ayache, 7th February 2015
Courtesy Martin Westwood

CONTINGENT CLAIM. Portrait of a Philosophy Series I, 2012.

Gerald Nestler, CONTINGENT CLAIM. Portrait of a Philosophy Series I. Elie Ayache.
1-channel video, 35:23 min., 2012.
Courtesy the artist.