Sunday, January 27, 2008

Drowning in the Black Scholes

As a one-time Mathematician and keen observer of Financial madness, I very much enjoyed reading an article that brought the two together.

Financial derivatives traded on capital markets can be really quite complex, but in fact the ones cack-handedly traded by the French rogue-trader were about as simple as they come.

When you read "Derivative", think "Health Insurance". With Health Insurance it is money down the drain if you "win" (i.e don't get sick) and a considerable comfort if you "lose". This consolation-prize approach is known as "Hedging". You can hedge a little of the risk, or all of the risk, or in the case of our "crazy frog", you can over-hedge for reasons not yet known and end up losing billions.

So how much should insurance companies charge for "Health Insurance" ? If the price is too high you'd be better off taking the risk of getting sick and insurance companies would never sell any policies.

There's some heavy-duty Nobel Prize-winning Mathematics called the Black-Scholes equations that put values on such things. I find the languages of these equations surprising : who would have predicted that chemistry terms such as "Brownian motion" and "Diffusion" would make an appearance in a Financial problem ?

Bizarrely enough this is because the equations turn out to be a special case of something more general in Mathematics called Heat Equations which were originally used to model the flow of heat in two objects of different temperature placed next to each other. Or,as Albert Einstein put it in his 1905 paper : "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen." Quite.

The important thing to remember here is that no matter how many Maths PhDs and computers the traders throw at the Financial Markets, they will never quite be able to reduce them to the predictability of two bits of hot metal.

Humans are involved in Financial Markets, and some of these are quite, quite mad.

1 comment:

Flitcraft said...

Brilliant - quality stuff!