is Black Scholes Accurate?

is Black Scholes Accurate?

The Black-Scholes formula has a peculiar status in modern science:

It is simultaneously extraordinarily important (and crowned with a Nobel prize in Economics) and woefully flawed.

A black and white photo of a bearded man in his fifties sitting in a chair.
Wilhelm Röntgen received the first Physics Nobel Prize for his discovery of X-rays.

It is always difficult to row against the flow. But, as I have repeatedly (and, I admit, rather unsuccessfully) argued over the last thirty years, I think far too much intellectual capital has been devoted to both refining and fudging the Black-Scholes model, in a desperate attempt to “fit option smiles” and price and hedge ever more exotic portfolios of derivatives. 

is Black Scholes Accurate?

In my humble opinion, post-Black-Scholes research should have recognized that markets are not and cannot be complete, and abandoned the perfect replication fallacy and the obfuscating “risk neutral probability” mantra.

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Responsible financial engineering should be about understanding how markets really work; the role of impact and feedback loops that generate non-Gaussian fat-tails; and estimating true risks rather than comfortably preserving the convenient tenets of the Black-Scholes world and turning a blind eye to its glaring inadequacies.

Of course, the theory is mathematically beautiful and intellectually alluring. The cornerstone of its derivation, Ito’s lemma, is deceptively simple and in fact sweeps all subtleties under the rug. It is therefore much easier to teach the perfect world of Black-Scholes. Rather than trying to confront all the messy aspects of real price time series, imperfect hedging, non-unique prices, etc. 

But everything that is really interesting about option markets would not even exist in the Black–Scholes world. This is actually my main peeve: the intuition that is built from Black–Scholes‘ theory is often scathingly misleading and deceptive. 

Of course, models are always simplifications and approximations of reality, but, in my view, it is crucial that models should allow one to understand how the world really works, rather than make us believe in a fantasy. Reality should always supersede elegance or convenience. 

As Derman and Wilmott wrote in their “Modeler’s Oath” manifesto: *I will never sacrifice reality for elegance without explaining why I have done so*.

For more on this, see my piece in the Black-Scholes 50th anniversary issue of Wilmott Magazine: WILMOTT Magazine May 2023 – Black-Scholes 50th Anniversary Issue – Wilmott

Written by:

Jean-Philippe Bouchaud

Chairman & Head of Research

Capital Fund Management

is Black Scholes Accurate?

is Black Scholes Accurate?