Tuesday, April 08, 2008

Formulas Don't Kill Pocketbooks, Traders Kill Pocketbooks

There’s a fair amount of fluff developing out there about the current financial uproar and the role of “The Black-Scholes Option Pricing Model” (see e.g. useful commentary and refs here). Black-Scholes is a natural candidate for suspicion because (a) it’s hubba hubba; (b) it is (or seems) impenetrable; and (c) people remember it had something to do with the near-death experience of Long-Term Capital Management, Inc. There’s probably enough truth in each of those points to keep the meme airborne, but there may nonetheless some profit in trying to bring the discussion down to earth. So, a few first principles.

One: Black-Scholes is a device for pricing conditional claims (link). Example: Megabucks, Inc. sells for $100 a share. Here’s an offer to buy Megabucks at $150 any time in the next year? How much will you pay? You won’t pay more than $100—if you would, you might as well just buy the share. But you will pay something more than zero. You’ll buy the chance—the lottery ticket—that Megabucks at some point in the next year will trade at more than $150 a share—say, $175. If it does, you’ll exercise your right to buy at $150. And maybe you’ll turn around and sell a moment later for a $25 profit. That’s a conditional claim. They’re everywhere.

Two: the math behind Black-Scholes is pretty heavy lifting. But the intuition is pretty easy. Like I said, you’re buying the chance, the possibility, a piece of the upside. In a word, volatility. And by the way, if Black Scholes math is too hairy, there is an alternative route—binomial option pricing—which is mathematically less sophisticated, but in practical terms, even more useful.

Three. Of course Black-Scholes is imperfect. What model isn’t? Black himself wrote a clever article (can’t put my finger on it just now) on how to profit from the simplifications in his own model. Oh and by the way, garbage in, garbage out. A lot of traders (or salesmen) with proprietary models are trying to make their living by convincing you that Black-Scholes has a "secret flaw" which they have unearthed and will (under limited license, for a large fee) disclose.

Four: I like what Robert Merton said (quoted by Kedrosky here). Fancy financial engineering has not made the world more risky, but it has permitted us to take more risks. Every frontier is a horizon. My GPS, my cellphone, make me willing to take more risks on the road; fancy option models do the same work in the market.

Finally: I suspect one reason Black Scholes has a bad name is because people associate it (justly) with Merton, and because Merton and Scholes together get a large part of the blame for LTCM (see, e.g., here and here). Well, they deserve it, but it does not follow that their failure was a failure of the model. Indeed, one plausible view of the evidence is that they failed precisely because they forgot to learn their own lessons and set about flogging their supposed superior investment skill—the one thing a paure-analytic model tells you that you’re not supposed to do.

For extra credit: there’s great stuff on Black Scholes—and the context of finance theory generally—here.

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