Modeling the yield curve in conjunction with the FX spots

Abstract: Interest rates and foreign exchange spots are widely used within financial products. It is important to understand the risk arising from products that depend on interest rates and/or foreign exchange spots. In this project, the Hull-white model, a non-parametric and a semi-parametric bootstrap will be investigated for simulations of the interest rate of USD, EUR and SEK in conjunction with its corresponding foreign exchange spot. Models were first studied for dollar interest rates and the best model was selected by using variance/autocovariance tests and quantile tests. The chosen model was then used in the simulation of the interest rate in conjunction with the foreign exchange spots. The result from the tests demonstrated that the non-parametric bootstrap model performed the best and was used to simulate the interest rate in conjunction with the foreign exchange spots. The multiple simulations were used to back test a synthetic portfolio using a quantile test. The simulated distribution was found to be acceptable which therefore simulates an acceptable risk. We used data up until 2015 for the tests, this for not including the federal reserve raising the interest rate in the later part of 2015. Avoiding changes in the Fed funds rate was necessary as they are not predictable from sampling from historical data as is done in the model but they do have a very large impact on the shorter end of the curve. The findings in this project suggests that the non-parametric bootstrap model could be used in multiple curve simulations, which could be used for calculations of potential future risk for financial products. This is very important for companies involved with financial products, since strict rules and regulations have to be followed regarding risks within these products.