The VIX index, which is the expected volatility of the S&P 500 index in 30 days, is of interest to a lot of investors on the US financial market. Allowing the volatility of the financial market to be used as a trading tool gives rise to interesting investment opportunities, such as hedging and speculation. In this thesis we will be creating an investment strategy on VIX futures by modelling the term structure with a Bayesian approach. Using Markov Chain Monte Carlo (MCMC) methods, we will simulate a posterior distribution of our term structure, which results in credible intervals of our futures prices. We will compare the efficiency of Metropolis-Hastings algorithms against the No-U-Turn Sampler, which is a Hamiltonian Monte Carlo algorithm. Eventually we find that the No-U-Turn Sampler significantly outperforms the Metropolis-Hastings algorithms. The resulted credible intervals of our futures prices will be used to determine whether a contract is overvalued or undervalued. The strategy consists of taking a combination of long and short positions on VIX futures contracts which we consider to be mispriced. We will therefore take a long position on undervalued VIX futures, while taking a short position on overvalued VIX futures. We eventually find that this investment strategy is very risky due to the high volatile behaviour of the VIX index.

Time series analysis is used to predict future behaviour of processes and is widely used in the finance sector. In this paper we will analyse the modelling of multivariate time series of financial data using vector autoregressive processes. The goal is that the reader will understand the presented models and could theoretically perform time series analysis by himself. Two specific models will be explained: the Vector Autoregressive model (VAR model) and the Vector Error Correction Model (VECM). We will describe various methods to analyse multivariate time series using these models, such as forecasting the process, variance decomposition of the forecast error, causality analysis and impulse response analysis. Examples of these models and analysis methods will be presented and investigated. Finally, we will perform a time series analysis with these models on Dutch indices and stock data. We conclude that real-world data often does not fit the VAR model and VECM requirements and that further improved models should be considered as well.