## Monday, February 13, 2012

### Ian Stewart on Black-Scholes

$\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^{2}S^{2}\frac{\partial^{2} V}{\partial S^{2}}+rS\frac{\partial V}{\partial S}-rV=0.$
(Black-Scholes Equation)

Good piece (as usual) from Ian Stewart on some of the mathematics underlying the financial crash:

http://www.guardian.co.uk/science/2012/feb/12/black-scholes-equation-credit-crunch

From the article:
"Anyone who has followed the crisis will understand that the real economy of businesses and commodities is being upstaged by complicated financial instruments known as derivatives. These are not money or goods. They are investments in investments, bets about bets. Derivatives created a booming global economy, but they also led to turbulent markets, the credit crunch, the near collapse of the banking system and the economic slump. And it was the Black-Scholes equation that opened up the world of derivatives."