Dutch pension funds are under the supervision by De Nederlandsche Bank (DNB) and they must adhere to the Financial Assessment Framework (FTK), which outlines the methods for calculating liabilities, buffer reserves, and risk factors. As part of the FTK, a feasibility test must be performed, which is a scenario-based analysis of pension funds' investment strategies and their pension policies based on economic scenario sets projected 100 years into future. Every quarter, DNB publishes these economic scenarios (P-scenarios) and equivalent risk-neutral scenarios (Q-scenarios) are used to calculate the effects of the pension fund reform in the Netherlands. These scenarios are generated by a stochastic model, which is revised every 5 years by a commission appointed by the Dutch government, called the Commission Parameters. The model currently in use is based on Commission Parameters 2022 and is referred to as CP2022.

The CP2022 model is an affine and arbitrage-free model framework for correlated interest rate, inflation rate, stock index and consumer price index, each being driven by Heston's stochastic volatility process. To generate realistic economic scenarios, the model is calibrated quarterly using bond and option market data. Currently, as part of the calibration process, option prices are computed under the dynamics stated by CP2022 using a Monte Carlo-based approach. As an alternative, we resort to a Fourier method called the COS method, which relies on the availability of the characteristic function of the state factors. We propose an efficient option valuation scheme for pricing European call and put options, and cliquet options under CP2022. Compared to the Monte Carlo method, our scheme demonstrates superior accuracy and computational efficiency.

We price continuously monitored barrier options under GBM and SABR through a newly developed neural network, the COS-CPD network, based on the COS-CPD method. With the pricing PDE and the COS method, we transform the problem of pricing the barrier options into a problem of finding the survival characteristic function through an initial boundary value problem. By applying trigonometric expansion, derived by integrating out the Fourier expansion on the time derivative of the unknown function, to the survival characteristic function, we find an approximation that can be inserted into the IBVP. Without CPD, this results in a linear system which can be solved to find the expansion coefficients, but this leads to the curse of dimensionality. If we include CPD to remove this curse of dimensionality, resulting in the COS-CPD network, the Alternating Least Squares method must be used to find the factor matrices that replace the original expansion coefficient tensor.

In this study, two interest rate models are analysed in context of counterparty credit risk. The goal of the study is to find a model that performs well on historical simulation for the PFE and EPE. The two models analysed are the Dynamic Nelson-Siegel model and the Displaced Diffusion model.
In the Dynamic Nelson-Siegel model, a Nelson-Siegel curve is fitted against the historical yield curves. The fit gives an historical series of the parameter values of the Nelson-Siegel curve, which are modelled via a stochastic process to obtain future yield curve predictions. In historical backtesting, the classic model using AR(1) processes for the parameters performs inadequate. Analysis on the underlying assumptions of the model show that the mean-reverting behaviour that is modeled is the cause. In addition the data is likely to feature heteroskedastic behaviour, which is not incorporated by the model. An adjusted model in which one parameter is modeled with a random walk with drift performs well on longer maturity rates, however shorter maturity rates are not modeled satisfactory.
The Displaced Diffusion model uses a lognormal diffusion process that is shifted to model Libor rates. As it is a Libor market model, all libor rates are modelled seperately using correlated Brownian motions. The shift parameter allows negative rates to be modeled, and is initially assumed constant. The backtesting results are mixed; some observed libor rates are modeled inadequately and some cannot be rejected to come from the Displaced Diffusion model and thus are modelled correctly. When backtesting the PFE, the results are good at the short term. At the 2-year window, PFE estimates are not always conservative but the number of excesses are of medium severity when compared to the probabilities used in the green-orange-red system dictated by the Basel committee for VaR backtesting.