The bond market is affected by the shortage of liquidity problem, which means that many bonds are not frequently traded. This implies that market data for these bonds are missing. This lack of data represent a problem for financial risk measures such as Value at Risk (VaR). This research provides the framework for the construction of a proxy which replaces the missing data with artificial data such that VaR can be calculated. The data used for the VaR calculation are bond z-spreads, which is a credit spread measure. This research represents an improvement of the current proxy methodologies under different aspects. A major improvement is provided by the usage of machine learning algorithms such as Random Forest, Support Vector Regression and CatBoost which significantly increased the predictive accuracy of the proxy. Another main difference from the current proxy methods relies in the prediction of z-spreads daily changes (shifts), instead of z-spread levels. This modification required a shift types assessment and it has been beneficial both for the proxy performance and for the VaR calculation. The main result of this thesis from a financial and statistical perspective is the theoretical and empirical convergence of the VaR obtained through the proxy with the VaR calculated with real market data.