The Heston model with Term Structure: Option Pricing and Calibration

This thesis addresses the calibration of the Heston model with term structure (i.e. with piecewise constant parameters) to a set of European option prices from the FX market. Several option pricing methods are discussed and compared, among which the COS method, Lewis' method and the Andersen QE Monte Carlo scheme. Several modifications are...

Numerical Pricing of Bermudan Options with Shannon Wavelet Expansions

This thesis is about pricing Bermudan options with the SWIFT method (Shannon Wavelets Inverse Fourier Technique). We reformulate the SWIFT pricing formula for European options to improve robustness, which allows us to heuristically select - and test the goodness - of all of the parameters a priori. Furthermore, we propose a simplified version of...

Radial basis functions for option pricing in insurance liabilities

This thesis discusses the valuation of embedded options in insurance liabilities using radial basis functions. For insurance companies, the valuation of embedded options is an important topic within risk management. This valuation can become too computationally heavy when nested Monte Carlo simulations are used. To overcome this computational...

Reduction of Computing Time for Numerical Pricing of European Multi-dimensional Options based on the COS Method

Numerical integration methods such as the Fourier-based COS method can be used for effciently and accurately pricing financial products. The COS method can be applied to options on one underlying stock as well as on multiple underlying stocks. However, this method suffers from an exponential increase in computational complexity as the dimensions...

Arbitrage-free methods to price European options under the SABR model

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...

Hardware Acceleration of Monte-Carlo Integration in Finance

This thesis describes FPGA-accelerated Monte-Carlo integration using adaptive stratified sampling. Monte-Carlo integration can be used to determine the value of integrals that have no closed form solution. In this work, the FPGA-accelerated design is used to determine the price of different types of financial options. The considered options are...

The Gibbs phenomenon in option pricing methods: Filtering and other techniques applied to the COS method

There are situations in which the COS method for option pricing has relatively slow convergence as a consequence of the Gibbs phenomenon. This thesis focusses on various methods to improve the convergence rate of the so called spectral methods. Note that we are not just interested in an accurate recovery, but that we also want to be able to...