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...

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...

A Fourier-based approach for valuing bonds with embedded options: an analysis of convolution- and cosine-based approximation methods using jump-diffusion models and extended with stochastic interest rates

Due to their attractive characteristics, convertible and callable bonds became a more important class of fixed-income products within the financial market. Therefore, the need for fair and accurate pricing of convertible and callable bonds increases. Where the convertible option can be considered as a right for the bondholder, the callable...

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...

Valuation of electricity storage contracts based on the COS method: with underlying polynomial electricity prices

In this thesis we introduce valuation techniques to price electricity storage contracts, where the electricity prices follow a structural model based on polynomial processes. In particular we focus on a Fourier-based pricing method known as the COS method, which performs impressively to price the contracts accurately. We provide details on how...

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...

Valuation of natural gas storage contracts with the COS method

Since the liberalization of the energy markets, the storage of energy is decoupled from the production and sales. In Western-Europe the storage of natural gas becomes more and more important because production fields get depleted and governments force companies to slow down their production because of tremors in the ground. Natural gas needs to...

The COS method for option valuation under the SABR dynamics

In this paper, we consider the COS method for pricing European and Bermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by...

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...

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...

A Benchmark Approach of Counterparty Credit Exposure of Bermudan Option under Lévy Process: The Monte Carlo-COS Method

An advanced method, which we call Monte Carlo-COS method, is proposed for computing the counterparty credit exposure profile of Bermudan options under Lévy process. The different exposure profiles and exercise intensity under different mea- sures, P and Q, are discussed. Since the COS method [1] delivers accurate Bermudan prices, and no change...

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...

Pricing swing options with the COS method

In dit verslag wordt een methode gegeven om de swing optie te prijzen met de COS methode. Eerst zal behandeld worden wat een optie is en hoe de COS methode werkt. Daarbij zullen ook enkele andere opties aan bod komen als voorbeeld.

The Heston model with term structure

The purpose of this project is to extend the Heston model in order to incorporate the term structure (TS) of the implied volatility surface. This includes implementing a TS within the Heston model and its calibration to a set of market instruments. The TS Heston model with piecewise constant parameters is implemented to match the TS and the COS...