The volatility surface

by: Jim Gatheral,Nassim Nicholas Taleb

Jim has given round six of these lectures on volatility modeling at the
Courant Institute of New York University, slowly purifying these notes. I
witnessed and became addicted to their slow maturation from the first time
he jotted down these equations during the winter of 2000, to the most recent
one in the spring of 2006. It was similar to the progressive distillation of
good alcohol: exactly seven times; at every new stage you can see the text
gaining in crispness, clarity, and concision. Like Jim’s lectures, these chapters
are to the point, with maximal simplicity though never less than warranted
by the topic, devoid of fluff and side distractions, delivering the exact subject
without any attempt to boast his (extraordinary) technical skills ...

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