The vanna - volga method for derivatives pricing.

Abstract

This Master thesis highlights some basic features and applications of the vanna-volga method and its accuracy when pricing plain vanillas and simple barrier options. In the paper we derive formulas for premiums of vanilla FX options using two versions of the vanna-volga method – the exact vanna-volga method and the simplified vanna-volga method. We review a very common vanna-volga variation used to price the first-generation exotics and the application of the vanna-volga method to construct the implied volatility surface. Furthermore, we briefly discuss a popular stochastic volatility model that aims to take the smile effect into account – the Heston model. Its accuracy and efficiency is further compared with that of the vanna-volga method. In the part of the thesis, which is devoted to calibration results, we compare the results obtained by the exact vanna-volga method, the simplified vanna-volga method and the Heston model. We also investigate the accuracy of the vanna-volga method applied to barrier options. All the plots and graphs in this thesis were produced by programs implemented by the author in MATLAB. These programs are available on request