Financial Babel

The mythical Tower of Babel was an enormous building designed to reach heaven. The story’s theme is competition between divine and human beings, the construction of the tower being a hubristic act of defiance against God. In recent history, humans have constructed many financial towers of Babel, seeking to defy risk and the uncertainties that underlie markets.

Unlike physical sciences bounded by actual phenomenon, social pseudo sciences, including economics and finance, entail a peculiar dialectic. Someone somewhere writes a paper. Someone somewhere else, either in the next room or half a world away, writes a paper citing the original, either agreeing or disagreeing with its arguments. If enough participants engage in the debate, then it becomes in varying stages a discussion group, a minor cult, an offshoot of an existing discipline or, in a few cases, an entirely new discipline.

This idea was the subject of a disarmingly short (6 page), simple yet intellectually puzzling short story by Jorge Luis Borges, the Argentinian writer, “Pierre Menard, the Author of Don Quixote". The story takes the form of literary criticism about the fictitious Pierre Menard, a 20th century French writer. The story describes Menard’s translation of Don Quixote, which in reality is a line for line recreation of the original. Ironic and humorous, the story raises profound questions about writing and interpretation.

Borges, writing as the reviewer, considers Menard’s Quixote to be much richer in allusion than the original text, to which it is identical. This reflects the context of the world and the author, which shapes the work. In “Pierre Menard”, Borges anticipated post-modern literary theory and philosophy.

Nassim Nicholas Taleb’s “Black Swan” is undergoing a similar developmental arc. If the Black Swan is Donald Rumsfeld’s Unknown Unknown, then the White Swan, a term now frequently used for anticipated crises, is the Known Unknown. There is also the Gray Swan, which presumably has elements of both. In “The Blank Swan”, Dr. Eli Ayache, a former derivative trader and principal of a software firm, extends the idea, perhaps creating the new discipline of “Cygnus Finance”.

“Pierre Menard” has its own history. In Italo Calvino’s “If on a Winter's Night a Traveleri”, a character, Silas Flannery, tries to copy a famous novel, “Crime and Punishment”, to assist his own writing. Gonzo journalist Hunter S. Thompson reportedly re-typed “The Great Gatsby” when studying at Columbia University. Intriguingly, Dr. Ayache’s critical analysis of “The Black Swan” was specifically structured around Borges’ “Pierre Menard”.

Dr. Ayache’s central thesis is that the existing approach to derivative pricing and, ultimately, probability at least as it applies to financial instruments, is incomplete and inherently inadequate. He sees the excesses of modern finance, such as CDOs and CDO2, as a manifestation of an underlying philosophy grounded in probability.

Traditional financial theory assumes that risk equates to standard deviation or variance of price changes in a Gaussian (standard distribution) probability framework. Option prices “derive” from the underlying. Options premiums are either an expression of expected volatility or the ability to dynamically recreate the instrument through trading in the underlying asset. Dr. Ayache argues that the price of stock or an option cannot be based purely on probabilities but must take into account the context. So probabilities are meaningless since contexts keep changing.

If a stock is priced at $10 based all the available information, then the price is a function of a unique context and assigned probabilities are only valid for that context. As economic, political and social variables change, new contexts are created. In the new context, the original probabilities may become meaningless, requiring the creation a new set of probabilities to model the new scenarios. In addition, the premise of acting in the market to hedge options of itself changes the context, creating an inherent circularity. The title “Blank Swan” reflects the fact that as these contexts change unexpectedly and unpredictably, the original probability and its very idea become increasingly meaningless.

Dr. Ayache’s solution is to bypass the probability conundrum. He would prefer to think of all options as a special case of a deeper generalised problem of contingent claims. Pricing then becomes a function of what people today value different payoffs, using any tractable logical framework available. At an extreme, this implies that there is a market price for a contingent claim that exists independently of probability or options.

This recognises a truth that anyone who trades option understands – option pricing models don’t price options, instead traders use models to recovery the equivalent volatility (the probability parameter) for a given option premium, frequently to derive the delta and other Greeks for hedging. “The Blank Swan” thesis is reminiscent of the advice of Jacobi, the Prussian Mathematician, to always invert to solve the problem.

The thesis is developed through discursive discussions of philosophy, literature, film and practical issues, arising from a trip to a client in Sydney Australia. The book’s approach owes a considerable debt to Roland Barthes’ textual analysis and the French Deconstructivist philosophers, like Derrida.

The writing style is dense, matching the challenging content. Dr. Ayache told one interviewer that he tends “to write only the things that will be as difficult to read as they were to write.” Paul Wilmott, the respected derivative researcher, advises on the cover that the book is not recommended beach reading. He counsels reading its in front of a log fire with a large Scotch or several.

Economics developed out of political thought and philosophy, eventually branching into macro and microeconomics. Microeconomics spawned financial economics and quantitative finance. In turn, there is now financial sociology and financial philosophy. “The Blank Swan”, like its namesake “Black Swan”, may be part of that evolution.

Borges in another short story “The Library of Babel”, similar to his essay “The Total Library”, wrote about the impoverishment of text through the means of its reproduction. All texts are reproduced in a vast library only because complete randomness eventually produces all possible combinations of letters. Like “Pierre Menard”, “The Library of Babel” explores the complex nature of meaning. In “Pierre Menard” meaning depends on context of the work while in “The Library of Babel” meaning is a function of randomness, as the library contains all possible works. “The Blank Swan” can be interpreted as “Pierre Menard”, “The Library of Babel” or both.

In post modern thought, there is anxiety about the nature of reality. As in all modernism, the problem in finance is the meta level. Modern meta finance creates instruments, like options, abstracted from real things, making traditional concepts of money otiose. In post modernity, the meta level eventually dominates the primary level that it emanates from. Candy floss money of derivatives and securitisation dominates ordinary money creating circularity and self reference.

Value becomes driven by itself. New instruments emerge, being traded in huge volumes amongst institutions essentially trading with themselves. They undertake transactions, price them and book fictitious earnings, neglecting to establish whether any of it is real or makes economic sense. The function of money markets to raise and invest money is undermined. The true function of money as a mechanism for exchange, a store of buying power and a measure of value is corrupted.

The significance of “The Blank Swan” is difficult to know, at least now. In another Borges short story “Death and the Compass”, detective Erik Lönnrot attempts to solve a mysterious series of murders which seem to follow a kabbalistic pattern. The detective finds that his enemy Scharlach has set a trap counting on Lönnrot’s overly developed intelligence to read into the events a pattern. The detective’s over-intellectualising leads to his death.

Could it be that “The Blank Swan” over-intellectualises and creates it own labyrinth from which it cannot escape? After all, financial markets exist simply to facilitate investing and borrowing or make items tradeable to facilitate speculation. The rest, as they say, is “noise”.

Another alternative is Borges’ story “The Garden of the Forking Paths”. Based on the concept of parallel worlds, Borges outlines a series of infinite paths or sequences of events, in which every alternative can co-exist. As we can only take a singular path, our history seems concrete and definitive when it is merely one of a number of possibilities. Has the world of economics and finance already taken a path in which probability, ill considered and flawed as it may be, shapes our framework of activities? Or is there still time in this journey to re-shape our world in the way that “The Blank Swan” argues?

Robert Frost describes this choice in his poem “The Road Not Taken”. Dr. Ayache has taken the path “less travelled by” and that is an extraordinary act of courage and self belief.

© 2010 Satyajit Das All Rights reserved. Satyajit Das is a risk consultant and author of Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives – Revised Edition (2010, FT-Prentice Hall).