Applying Multivariate Expected Shortfall on High Frequency Foreign Exchange Data

Sammanfattning: This thesis aims at implementing and evaluating the performance of multivariate Expected Shortfall models on high frequency foreign exchange data. The implementation is conducted with a unique portfolio consisting of five foreign exchange rates; EUR/SEK, EUR/NOK, EUR/USD, USD/SEK and USD/NOK. High frequency is in this context defined as observations with time intervals from second by second up to minute by minute. The thesis consists of three main parts. In the first part, the exchange rates are modelled individually with time series models for returns and realized volatility. In the second part, the dependence between the exchange rates is modelled with copulas. In the third part, Expected Shortfall is calculated, the risk contribution of each exchange rate is derived and the models are backtested. The results of the thesis indicate that three of the five final models can be rejected at a 5% significance level if the risk is measured by Expected Shortfall (ES0:05). The two models that cannot be rejected are based on the Clayton and Student’s t copulas, the only two copulas with heavy left tails. The rejected models are based on the Gaussian, Gumbel-Hougaard and Frank copulas. The fact that some of the copula models are rejected emphasizes the importance of choosing an appropriate dependence structure. The risk contribution calculations show that the risk contributions are highest from EUR/NOK and USD/NOK, and that EUR/USD has the lowest risk contribution and even decreases the portfolio risk in some cases. Regarding the underlying models, it is concluded that for the data used in this thesis, the final combined time series and copula models perform quite well, given that the purpose is to measure the risk. However, the most important parts to capture seem to be the fluctuations in the volatilities as well as the tail dependencies between the exchange rates. Thus, the predictions of the return mean values play a less significant role, even though they still improve the results and are necessary in order to proceed with other parts of the modelling. As future research, we first and foremost recommend including the liquidity aspect in the models.