Hedging of a foreign exchange swapbook using Stochastic programming

Sammanfattning: 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.