The Fundamental Theorem of Derivative Trading - Exposition, Extensions, and Experiments

27 Pages Posted: 18 Feb 2015

See all articles by Simon Nielsen

Simon Nielsen

University of Copenhagen - Department of Mathematical Sciences

Martin Jönsson

University of Copenhagen - Institute for Mathematical Sciences

Rolf Poulsen

University of Copenhagen - Department of Statistics and Operations Research

Date Written: February 17, 2015

Abstract

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 formula). We also consider its practical consequences both in simulation experiments and on empirical data thus demonstrating the benefits of hedging with implied volatility.

Suggested Citation

Nielsen, Simon and Jönsson, Martin and Poulsen, Rolf, The Fundamental Theorem of Derivative Trading - Exposition, Extensions, and Experiments (February 17, 2015). Available at SSRN: https://ssrn.com/abstract=2566425 or http://dx.doi.org/10.2139/ssrn.2566425

Simon Nielsen

University of Copenhagen - Department of Mathematical Sciences ( email )

Copenhagen
Denmark

Martin Jönsson

University of Copenhagen - Institute for Mathematical Sciences ( email )

Solbjerg Plads 3
Copenhagen, DK-2100
Denmark

Rolf Poulsen (Contact Author)

University of Copenhagen - Department of Statistics and Operations Research ( email )

Universitetsparken 5
DK-2100
Denmark
+45 (353) 20685 (Phone)

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