|Institution:||Delft University of Technology|
|Keywords:||option pricing; SABR; Fourier cosine expansion method; BCOS|
|Full text PDF:||http://resolver.tudelft.nl/uuid:ca07093c-44f1-40e6-8dc6-f01d9b7f61c8|
In this thesis we discuss several methods to price European options under the SABR model. In general, methods given in literature are not free of arbitrage and/or inaccurate for long maturities. This led to the development of a new pricing approach. We extend the BCOS method from one dimension to two dimensions. This extension is necessary for application of a simplification of the BCOS method, the DCOS method, to the SABR model. In this pricing method we use the characteristic function of the discrete forward process and the Fourier-based COS method. It is possible to price European options under the SABR model for multiple strikes in one computation with the DCOS method. Besides valuing European options, we can also price Bermudan and discretely monitored barrier options with this pricing approach.