A novel cosine network for pricing European and barrier options under stochastic volatility models

This thesis presents a comprehensive exploration of the rough Heston model as a means to enhance financial derivative pricing and calibration in the context of the complex behavior of market volatility. Recognizing the limitations of classical models, such as the Black-Scholes and the standard Heston model, which assume constant or mean...

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...

Pricing Barrier Options under Lévy Processes using Dimension-reduced Cosine Expansion

Barrier options are fundamental financial tools that give rise to pricing challenges, particularly when embedded within stochastic models. This study directs its focus towards Lévy processes as a strategic approach to navigate and resolve these intricate complexities. The model assumption adopted in this thesis is that the underlying log-asset...

Solving multivariate expectations using dimension-reduced fourier-cosine series expansion and its application in finance

The computation of multivariate expectations is a common task in various fields related to probability theory. This thesis aims to develop a generic and efficient solver for multivariate expectation problems, with a focus on its application in the field of quantitative finance, specifically for the quantification of Counterparty Credit Risk (CCR...

Dimension reduction techniques for multi-dimensional numerical integrations based on Fourier-cosine series expansion

A wide range of practical problems involve computing multi-dimensional integrations. However, in most cases, it is hard to find analytical solutions to these multi-dimensional integrations. Their numerical solutions always suffer from the `curse of dimension', which means the computational complexity grows exponentially with respect to the...

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...

Fast Calculations of Portfolio Credit Losses and Sensitivities

Computing portfolio credit losses and associated risk sensitivities is crucial for the financial industry to help guard against unexpected events. Quantitative models play an instrumental role to this end. As a direct consequence of their probabilistic nature, portfolio losses are usually simulated using Monte Carlo copula models, which in turn...