## ‘Wrong’ economic theories and performativity: reply to Ezra

### October 28, 2008

*This post started as a reply to a post on OrgTheory**, but it got slightly longer and raised some interesting issues, so I thought that I’d make a post out of it. *

*Let me give you the context. The issue here is the question of whether or not a ‘wrong’ economic theory can be performed in such a way that it ‘becomes’ accurate. I claimed that Black-Scholes-Merton is an example (in fact, a very good example) for a wrong, but very successful, economic model. Ezra answered that “The inaccuracy of BSM at the outset was not a surprise to anyone because it was not a descriptive theory, but a prescriptive one- a model for what one *should* do. After all, the options market basically did not exist when the theory was developed, so it could not have been intended as description.”*

*Below is my answer to Ezra*

Ezra, I see what you mean now. However, Black-Scholes-Merton is a good example of a wrong model that ‘became accurate’ and that’s for two reasons: I would call them the ‘weak’ reason and the ‘strong’ reason.

First, the ‘weak’ reason. Yes: an organised options market did not exist when the model was published and the assumptions underpinning the model did not exist in the market even when it was established (i.e. no restriction on short selling, no fees on borrowing, continuous trading). So, from this respect you can say that the model, like many other economic models, was talking about a ‘would be’ or a ‘utopian’ market rather than an existing one. That, of course, does not turn the model into a prescriptive model. No one in the Chicago options’ market or at the SEC used the model with the intention to prove that Black, Scholes and Merton were right. They used the model for a variety of reasons, most of which are related to operational efficiency. As the performativity thesis claims, an economic theory becoming accurate is a result of a networked emergence rather than the outcome of specific agents.

Now, for the ‘strong’ reason. The original, theoretically driven Black-Scholes-Merton model was based on a lognormal distribution of the underlying stock (the theory here goes all the way back to Bachelier, tying the movement of stock prices to Brownian motion, etc). Without this assumption at its basis, the model would be not much more than a fancy card trick run on high power computers. But, guess what… Nowadays, virtually no one uses the plain vanilla (but theoretically justified) lognormal distribution in his or her BSM-based applications. Since the crash of 1987, where the Black-Scholes-Merton was not accurate, the ‘engine’ of the model, if you like, was replaced by a variety of different distributions, none of them justified by the theoretical roots that led to Scholes’ and Merton’s Nobel prize. So, again, for a very long time (at least since the early 1990s) the Black-Scholes-Merton model has been ‘wrong’ theoretically, but useful operationally.

October 29, 2008 at 12:26 am

“Without this [lognormal distribution] at its basis, the model would be not much more than a fancy card trick run on high power computers”

I think this statement is overkill. The BS insight isn’t that stocks are lognormal – it’s that any derivative can be replicated out of a position in a stock of the underlining and a bond. (In fact, to get technical nerdy, the initial PDE proof only needs a distribution that is twice differentiable. The real insight of BS doesn’t even need lognormal! To get a functional equation you do though…)

As far as this quant feel (though I speak for many), that’s the real magic and contribution of the BS equation – the ‘engine’ if you will. And it is still the ‘theory’ basis of all finance; as far as a binomial tree or monte carlo or any of the practical current option tools, they are definitely using that ‘engine’ of dynamic replication, and of delta/gamma/vega/etc. hedging. It’s right in theory but useless in practice (can’t do American options, correlations, etc.)

October 29, 2008 at 12:29 am

Sorry – take out the technical nerdy () part. That’s not accurate – the rest stands though.

October 30, 2008 at 12:45 pm

Mike – I agree completely about the fact that the most influential element, from a practical perspective, is BSM’s replication of portfolios. In fact, this element is what drove the institutionalization of BSM, and, consequently, contributed to the formula to ‘became’ more accurate.

November 3, 2008 at 3:39 am

[…] Wrong Economics Theories and performativity – Via Socializing Finance – Let me give you the context. The issue here is the question of whether […]

December 13, 2008 at 8:13 pm

Pingback from multi-Criteria blog:

http://multicriteria.blogspot.com/2008/12/some-posts-on-same-subject.html

December 14, 2008 at 6:37 pm

Mike – Every time I’m talking to a quant I hear the same words over and over again. Where it is written in stone that the only mathematical apparatus available for pricing models is that of probability theory? The ‘engine’ you reference to is ineffective because it forces unacceptable assumptions from the very beginning. The “operational usefulness” notion mostly comes from those physics PhD’s Taleb kept hunting for in JFK. Industry just doesn’t know any better.

April 15, 2009 at 5:42 pm

This topic is quite hot in the net right now. What do you pay attention to when choosing what to write ?