Quantitative Finance in a Nutshell

Just what does it mean to be a quant? In his December 2002 article entitled “The Boy’s Guide to Pricing & Hedging “, Emanuel Derman offers an “abbreviated poor man’s guide” to quantitative finance. He observes that:

“To begin with, you must distinguish between price and value.”

“If you want to know the value of a security, use the price of another security that’s as similar to it as possible. All the rest is modeling. Go and build.” This precept is an operational statement of the law of one price or the principle of no risk-free arbitrage.

“The law of one price is not a law of nature. It’s a general reflection on the practices of human beings, who, when they have enough time and enough information, will grab a bargain when they see one.”

“If you want to estimate the value of a target security, the law of one price tells you to find some other replicating portfolio, a collection of more liquid securities that, collectively, has the same future payouts as the target, no matter how the future turns out. …It takes a model…”

“But no mathematical model will capture the intricacies of human psychology. If you listen to the models’ siren song for too long, you may end up on the rocks or in the whirlpool.”

“…as Paul Wilmott aptly expressed it, ‘every financial axiom…ever seen is demonstrably wrong.’ Therefore, quantitative finance practitioners need to know where best to spend their effort in the grittily messy world they inhabit. In preparing for that world it’s best to start with the concrete and then proceed to the abstract.”

In summary, quantitative finance is an emphatically empirical field focused on finding bargains by comparing the prices of similar assets, and safely skimming returns from these bargains.

The article is short and readable, including simple examples for bonds, stocks and derivatives.

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