Realistic Modeling


“Economic Realism (Wonkish)”, a blog entry by Paul Krugman in The New York Times, discusses a paper, “Chameleons: The Misuse Of Mathematical Models In Finance And Economics”, by Paul Pfleiderer of Stanford University, which surprises me by including a color picture of a chameleon right there on the front page, and in an academic paper at that, and I didn’t know you could have color pictures included just for their visual appeal in academia these days. Anyway, Pfleiderer discusses the difficulty of what they term filtering, making sure that the assumptions one makes to build a model — which are simplifications and abstractions of the real-world thing in which you’re interested — aren’t too far out of line with the way the real thing behaves.

This challenge, which I think of as verification or validation, is important when you deal with pure mathematical or physical models. Some of that will be at the theoretical stage: is it realistic to model a fluid as if it had no viscosity? Unless you’re dealing with superfluid helium or something exotic like that, no, but you can do very good work that isn’t too far off. Or there’s a classic model of the way magnetism forms, known as the Ising model, which in a very special case — a one-dimensional line — is simple enough that a high school student could solve it. (Well, a very smart high school student, one who’s run across an exotic function called the hyperbolic cosine, could do it.) But that model is so simple that it can’t model the phase change, that, if you warm a magnet up past a critical temperature it stops being magnetic. Is the model no good? If you aren’t interested in the phase change, it might be.

And then there is the numerical stage: if you’ve set up a computer program that is supposed to represent fluid flow, does it correctly find solutions? I’ve heard it claimed that the majority of time spent on a numerical project is spent in validating the results, and that isn’t even simply in finding and fixing bugs in the code. Even once the code is doing perfectly what we mean it to do, it must be checked that what we mean it to do is relevant to what we want to know.

Pfleiderer’s is an interesting paper and I think worth the read; despite its financial mathematics focus (and a brief chat about quantum mechanics) it doesn’t require any particularly specialized training. There’s some discussions of particular financial models, but what’s important are the assumptions being made behind those models, and those are intelligible without prior training in the field.

Advertisements

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

2 thoughts on “Realistic Modeling”

  1. Thanks a lot for this pointer! (Mis-)used of physics analogies and related models in finance is something I am very interested in.

    As fan of Nassim Taleb’s writings I am totally wary of such models. I would like to learn more about the history of modeling though, and I might read “The Physics of Wall Street” by James Owen Weatherall someday.

    My current bias is that Wall Street quants are often former physicists who still indulge in playing with some intricate differential equations as they did in academia. But the consequences – when their calculations finally have an impact on real-world financial products – are more far-reaching.

    Like

    1. I’ve gotten awfully interested in mathematical finance but fear I’ve got too much basic material to learn to get to the really interesting stuff.

      My only real squabble with the Wall Street quants, apart from their destroying the world’s economy, is that their existence has given my father the idea that since I know mathematics, and they do mathematics, I just need to whip up an algorithm and start collecting quarter-million-dollar paychecks. As best I can figure it isn’t quite that straightforward, unfortunately.

      Like

Please Write Something Good

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s