Talk on The Fundamental Theorem of Derivative Trading
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.