Solving the partial differential equation for pricing barrier options via trigonometric expansions

Barrier options, although highly liquid financial derivatives, present notable pricing challenges. In this thesis, we present a novel pricing approach for valuing continuously-monitored knock-out barrier options within the framework of stochastic volatility models.<br/><br/>The underlying process is firstly modelled under geometric Brownian...

Replacing the Monte Carlo Simulation with the COS Method for PFE (Potential Future Exposure) Calculations

To fulfil the need in the industry for fast and accurate PFE calculations in practice, a new, semi-analytical method of calculating the PFE metric for CCR has been developed, tested and analyzed in this thesis. Herewith we focus on the calculation of PFEs for liquid IR and FX portfolios involving up to three correlated risk-factors: a domestic...

European option pricing under the rough Heston model using the COS method

This thesis is about pricing European options using a Fourier-based numerical method called the COS method under the rough Heston model. Besides examining the efficiency and accuracy of the COS method for pricing options under the rough Heston model, it is also investigated if the rough Heston model produces the advantages of the so-called rough...