Introduction

Cryptocurrencies are digital currencies traded through privately owned exchanges. Retail and institutional investors are increasingly interested in this new asset class given its price growth in recent years as well as a means of portfolio diversification and risk management. Bitcoin (Nakamoto 2008) plays a leading role in cryptocurrency exchanges and its price movements have an impact across the whole market despite the existence of multiple competing cryptocurrencies (Kyriazis 2019). When adding a cryptocurrency such as Bitcoin to a portfolio, we need to be aware of its risk level. An important market risk metric of an investment \(Y\) is its Value at Risk at level \(\alpha\) or \(\text{VaR}_\alpha^Y\) as defined in equation (2.1). This metric represents what portion of a given investment is at risk given a probability level \(\alpha \in (0,1)\). \(\text{VaR}\) forecasting can be done using non-parametric, parametric or semi-parametric statistical models.

Ardia, Bluteau, and Rüede (2019) found an improvement over the benchmark GARCH(1,1) model for one day ahead \(\text{VaR}\) forecasting using a Markov–switching GARCH specification, implemented in the R MSGARCH package (Ardia et al. 2020) while Wang et al. (2019) used a multivariate extension of the original \(\text{CAViaR}\) model (Engle and Manganelli 2004) by White, Kim, and Manganelli (2015) to study the spillover effect from external markets and found that Bitcoin exhibits safe-haven like characteristics making it a good candidate for portfolio diversification. However, Bitcoins’ high volatility makes it a high-risk investment which has important implications from a risk management perspective for any financial institution interested in being exposed to this asset class. For instance, capital requirements as per the Basel accords are higher for cryptocurrencies (Stavroyiannis 2018).

The first chapter will introduce the mechanics of the blockchain technology upon which Bitcoin’s value is built both from a technological and a from historical perspective. Next, we present the statistical models and methods used to obtain a forecast for \(\text{VaR}_{t+1}\) based on the information set \(\mathcal{I}_t\). The last two chapters include a summary of the results obtained using different Markov Chain Monte Carlo (MCMC) estimation methods and applying those methods to a simulated dataset as well as real time data. These results have been summarized in the Simulation Study and Application chapters.

Different R packages are used for the Simulation study and Applications sections. These packages are text files containing source code written by their respective authors using mainly the R (R Core Team 2020) and C++ (Stroustrup 2013) programming languages. All source code used to produce this document is freely available online at https://cran.r-project.org/, the source code of the caviarma package (Chaparro Sepulveda 2019) and simulr package (Chaparro Sepulveda 2021) is available at https://gitlab.com/cacsfre. An interactive web version of this document can be found at https://cacsfre.gitlab.io/msc while its source code can be downloaded from https://gitlab.com/cacsfre/msc.