Consistent pricing of VIX options

Sammanfattning: This thesis is an extension from the thesis "To what degree is the VIX benchmark computed by CBOE representative of its definition?" presented on June 16 in 2018. The primary purpose of this thesis is to investigate a consistent way of Fourier pricing with the Heston model and whether or not the estimates can be improved by extending the amount of CIR processes in order to catch the non-linear behavior of VIX options. Beginning with a brief introduction, explaining the VIX and its theoretical calculations when following the Heston dynamics. The introduction paves way explaining the basic definitions used when defining the choice of the respective model. Later, an in depth analysis of the Fourier Gauss-Laguerre algorithm when pricing European type put and call options will be thoroughly explained. Finally, discussions regarding the parameter estimates as well as extensions of vol-of-vol terms will be further scrutinized.