The Fundamental Theorem of Derivative Trading - Theory and Applications

Resume: When European options are hedged with a misspecification of the volatility it leads to a non-zero profit-loss of the delta hedged option portfolio. In this thesis the dynamics and present value of the hedge portfolio are derived in three models; the Black-Scholes model, Merton’s jump-diffusion model, and Heston’s stochastic volatility model. This leads to three versions of the Fundamental Theorem of Derivative Trading, and simulation experiments are conducted in order to test the implications of the result. Moreover, it is investigated how the profit-loss behaves over time when options on the S&P500 Index are hedged over the period 2004-2013. For all types of hedges considered in this thesis there is a negative volatility risk premium embedded in at-the-money call options caused by implied volatility being larger than realized volatility. Additionally, indications of an even higher premium can be detected in out-of-the-money put options. Using the VIX Index as the variance process in Heston’s model is the preferred hedging strategy when comparing the variance of hedging errors and quadratic variation of daily changes in the profit-loss 

Vejleder: Rolf Poulsen
Censor:  Cathrine Jacobsen