A large part of the foreign exchange market concerns the trading of FX swaps. While entering a position in a FX swap does not cost any money, banks earn money on FX swaps when their customers cross the bid/ask spread, creating a perceived transaction costs for the swaps. To hedge the risks of their customer positions, banks enter new positions in FX swaps with other banks, crossing the same bid/ask spread. Traditional hedging methods does not take perceived transaction costs into account when determining hedge positions, resulting in greater portfolio losses than necessary for the banks. Therefore, the topic of hedging while taking transaction costs into account could be of great value. When valuing FX swaps and estimating risk factors in a FX environment, term structures need to be estimated for pricing the instruments. The estimation of term structures can be done using several ap- proaches, among them bootstrapping and interpolating the curve or parameterizing the curve, assuming it to be described by a functional form. These traditional methods of term structure measurement has the downside of being unstable and fluctuating greatly over time because of different local optimas each day, or result in very large pricing errors due to certain instruments needing to be excluded from the term structure measurement. These attributes result in capturing extra, unnecessary volatility in the curves which does not model the true risk, consequently estimating the risk factors wrongly when risk management and hedging needs to be done. The estimation of good quality term structures which are stable over time and result in low pricing errors are therefore of great interest to study. In this thesis, a FX swap portfolio is hedged using a Stochastic Programming (SP) model developed by Blomvall and Hagenbj ̈ork (2020). For the valuation of FX swaps in the portfolio and the generation of risk factors for the model, term structures were estimated using a multiple yield curve framework of Blomvall and Ndengo (2013), which penalizes pricing errors and use regularization functions to produce smooth curves. For both the term structure measurement method and the hedging method, a critical part affecting the per- formance of the methods lies in choosing good parameter values, which is what has been the main purpose of this study. The results show that good quality term structures can be estimated using the multiple yield curve frame- work if good parameter choices are made. The resulting curves fulfill the criteria of being stable over time while also keeping the price errors out-of-sample small. A portfolio hedged using a SP-model with certain chosen parameter values and also using the good quality term structures estimated is shown to eliminate a great deal of risk compared to an unhedged portfolio. When compared with a traditional hedging model called the Boxes model, the SP-model gains value from taking perceived transaction costs into account and thus manages to hedge the risks less costly than the Boxes model does.

The global foreign exchange (FX) market is one of the world's largest financial markets and a significant part of this market concerns the trading of FX swaps. For banks and other financial institutions, it is of great interest to model these swaps as accurately as possible, as this could improve their risk management. Numerous methods exist for modeling FX swaps, but it is not always clear if one model is superior to another. The purpose of this thesis is therefore to analyze, evaluate and compare different models that represent the stochastic processes in the FX swap market. To accomplish this, the thesis employs the reality model evaluation methodology developed by \citet{Blom_fx_pdf}. With this methodology, likelihood values for an out-of-sample period can be determined for a model, thereby enabling a statistical comparison to ascertain which model more accurately reflects the true distribution. This thesis will compare two models for FX swap prices: an interest rate model and a PIP-model. The PIP-model is constructed by determining a multivariate distribution based on in-sample observations of pips. The likelihood values for the out-of-sample observations can therefore be determined directly. The interest rate model, on the other hand, will be implemented using Blomvall's reality model evaluation in order to determine the likelihood values. It is constructed by evaluating risk factors of the FX swaps, rather than historical pips. The risk factors evaluated in this thesis are forward curves, the spot price and spikes in the supply and demand curve at certain dates. The results show that the interest rate model better represents the true distribution of FX swaps compared to the PIP-model. The statistical test of the out-of-sample likelihood values shows that the probability of the interest rate model outperforming the PIP-model is approximately 100 \%. Additionally, the result suggests that an implementation of the interest rate model using a Student's t-distribution is more advantageous than using a normal distribution, a conclusion also supported by a statistical test. Moreover, the effectiveness of Blomvall's reality model evaluation in determining likelihood values is confirmed, thus enabling the statistical comparison of different models.

Market makers such as large banks are exposed to market risk in fixed income by acting as a counterparty for customers that enter swap contracts. This master thesis addresses the problem of creating a cost-effective hedge for a realistic swap book of a market maker in a multiple yield curve setting. The proposed hedge model is the two-stage stochastic optimisation problem created by Blomvall and Hagenbjörk (2020). Systematic term structure innovations (components) are estimated using six different component models including principal component analysis (PCA), independent component analysis (ICA) and rotations of principal components. The component models are evaluated with a statistical test that uses daily swap rate observations from the European swap market. The statistical test shows that for both FRA and IRS contracts, a rotation of regular principal components is capable of a more accurate description of swap rate innovations than regular PCA. The hedging model is applied to an FRA and an IRS swap book separately, with daily rebalancing, over the period 2013-06-21 to 2021-05-11. The model produces a highly effective hedge for the tested component methods. However, replacing the PCA components with improved components does not improve the hedge. The study is conducted in collaboration with two other master theses, each done at separate banks. This thesis is done in collaboration with Swedbank and the simulated swap book is based on the exposure of a typical swap book at Swedbank, which is why the European swap market is studied.

By issuing interest rate derivative contracts, market makers such as large banks are exposed to undesired risk. There are several methods for banks to hedge themselves against this type of risk; one such method is the stochastic programming model developed by Blomvall and Hagenbjörk (2022). The effectiveness of their model relies on accurate pricing of interest rate derivatives and risk factor analysis, both of which are derived from a term structure. Blomvall and Ndengo (2013) present a discretized multiple yield curve framework for term structure measurement that allows for price deviations. The model uses regularization to deal with noise inherent in market price observations, where the regularization counteracts oscillations in the term structure and retains the smoothness of the curve by penalizing the first and second-order derivatives. Consequently, the resulting model creates a trade-off between a smooth curve and market price deviations. Changes in policy rates adjusted by a country’s central bank significantly impact the financial market and its actors. In this thesis, the model developed by Blomvall and Ndengo (2013) was further extended to include these steps in conjunction with monetary policy meetings. Two models were developed to realize the steps in the risk-free curve. The first model introduced an additional deviation term to allow for a shift in the curve. In the second model, the weights in the regularization were adjusted to allow for rapid changes on days surrounding the closest monetary policy meeting. A statistical test was conducted to determine the performance of the two models. The test showed that the model with adjusted regularization outperformed the model with an additional deviation term as well as a benchmark model without steps. However, both step models managed to reduce in-sample pricing errors, while the model with an additional deviation term performed worse than the benchmark model for out-of-sample data, given the current parameter setting. Other parameter combinations would potentially result in different outcomes, but it remains conjectural.