To what degree is the VIX benchmark computed by CBOE representative of its definition?

Sammanfattning: The purpose of this paper is through an empirical approach understand the dynamics of VIX and investigate to what degree the benchmark computed by CBOE is representative of its definition. The method implemented is of a design where one constructs a hypothetical world in which synthetic options data are produced by the Bates-Heston model. This implies an underlying and known volatility with chosen parameters κ and θ for which a theoretical reference VIX can be produced and compared with the VIX benchmark following CBOE´s computational method. Furthermore the thesis investigates a real life manip- ulative accusation of the VIX. The investigation relies heavily on the moral hazard occurring when the manipulation is done by the book. The investigation yielded an in-depth derivation of the VIX index definition using the Bates-Heston model coupled with Carr’s formula. The results further showed that the CBOE computed VIX and theoretical reference VIX coincide with the greatest deviation occurring with a value slightly greater than 0.02, arguing for the CBOE computed VIX to be representative of its definition. Al- though the manipulation might not be as easy as one might think. The vast structure of the VIX calculations makes it hard trying to force arbitrage oppor- tunities.