Like Paul, I have been thinking a lot about what makes a good model and what makes a bad one. In physics or even biology, theories can come pretty close to being indistinguishable from the real thing. (Tables ARE made of atoms. Avoid the temptation to think about this or you will lose your footing.) Models are different, and are by definition not the real thing. They are simplifications, more or less gross as the case may be. (Stock prices do NOT evolve lognormally).
What is good simplification?
Axiom 1: All models sweep dirt under the rug.
Axiom 2: A good model makes explicit the dirt swept away.
For that reason, and despite the campaign to discredit it, and no matter what it’s creators think or say about it, I like Black-Scholes: it’s an idealized recipe for creating an option, a piece of engineering. The assumptions are very clear, and so you know what you are taking for granted when you use the model, and you know what has been swept out of view. It’ s your job to figure out how well the world matches its assumptions, and what to do about the mismatches. I beg your pardon, its creators should say and believe, I never promised you a rose garden.
www.edge.org asked a bunch of people to guess what would be the biggest scientific game-changer in their future: http://www.edge.org/q2009/q09_index.html.
Here’s my answer: http://www.edge.org/q2009/q09_7.html#derman
Happy New Year and I hope for less dirt under everyone’s rug, or failing that, better vacuum cleaners.
Originally published at Wilmott.com and reproduced here with the author’s permission.