CHAPTER 5Deriving Derivatives

“The underpinning of quantitative finance is arbitrage pricing theory. The fundamental assumption is that markets are efficient.”

—Response to the survey question: “How would you describe quantitative finance at a dinner party?” at wilmott.com

“We shape our tools, and afterwards our tools shape us.”

—Marshall McLuhan, Understanding Media: The Extensions of Man

Once the markets had a model for valuing derivatives there was no longer any excuse for not trading them. The market in options exploded. New financial instruments were created using the same kinds of mathematical model… new and increasingly complicated instruments. As the instruments got more complicated, so did the mathematical models. Where once there were traders in Savile Row suits drinking far too much at lunchtime, now there were geeks with badly fitting suits and PhDs. If you had a degree in mathematics or physics, then a job as one of those geeky quants became your goal.

A framework for valuing derivatives was all that was needed to ignite the fuse that led to the explosion in new and increasingly complex derivative contracts. The gullible might say that having a decent theoretical foundation for valuation and risk management allowed quants to create new instruments with known characteristics and whose risks could be understood, measured, and controlled. The cynical might say that having a foundation, any foundation, even the shakiest and dodgiest on sandy soil, over a defunct ...

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