On financial models: practice vs. theory
October 2, 2008
A comment on an previous post on SocFinance just reminded me there is life outside the Wall Street bailout. The post, titled “Emanuel Derman on the Accuracy of Models,” engaged some fascinating criticisms by Emanuel Derman and Nassim Taleb of financial models, which are very much consistent with Yuval’s.
My original post ended with an open question: what is the practical usefulness of theoretically correct models? To this question, Derman just offered his own answer:
In answer to the question” what is the practical accuracy of a theoretically correct model?” I ask “What do you mean by ‘correct’”?
Rather than reply with a difficult-to-see comment, I took it as an opportunity to write new post.
What do I mean by “correct”? What I have in mind is the distinction between functional relationships and specific values. For instance, Black-Scholes can be though of a model that, essentially says the following:
where y equals option value, and x equals the future volatility of the underlying stock. Let’s assume this is true (and the readers of MacKenzie and Millo know it’s not, but bear with me).
How useful is this? Very useful, one would think. If you want to know y, all you need is to find out x, and you’re done. But this overlooks the problem of estimating x. Now, a rational expectations model would argue that market actors will, over time and through trial and error manage to develop unbiased estimates of x. In practice, however, things are not so easy. Market actors may make mistakes, and x itself is probably a function of other parameters… the model of which could be unknown, or unstable over time.
My point, then, is that even if the original model, f(x), is correct, putting it to work still is problematic.
How do you get around that problem? Following my own research, what I’ve seen is that arbitrageurs on Wall Street use models in a different way — to reflect on their own estimates by looking at the implied estimates that their competitors developed. This is called “backing out” x.
But — wait! This itself creates a new problem. If you use the model to bet on y as well as to back out x from the prices of y, the same model is being used for two different things… to represent x, and to intervene in y. And this, in turn poses new and fascinating epistemic challenges. Stay tuned.