HIPERFIT Seminar Talk: The Fundamental Theorem of Derivative Trading - Exposition, Extensions, and Experiments

Presenter: Rolf Poulsen, Professor, Math/University of Copenhagen

Time: Tuesday, April 14, 15:00-16:00

Place: Aud 07 (HCØ, Universitetsparken 5)


When estimated volatilities are not in perfect agreement with reality, delta hedged option portfolios will incur a non-zero profit-and-loss over time. There is, however, a surprisingly simple formula for the resulting hedge error, which has been known since the late 90s. We call this The Fundamental Theorem of Derivative Trading. This paper is a survey with twists of that result. We prove a more general version of it and discuss various extensions (including jumps) and applications (including deriving the Dupire-Gyöngy-Derman/Kani formula). We also consider its practical consequences both in simulation experiments and on empirical data thus demonstrating the benefits of hedging with implied volatility. The paper is available online.


14 April 2015