Revisiting the methodology and application of Value-at-Risk

The main objective of this thesis is to simulate, evaluate and discuss three standard methodologies of calculating Value-at-Risk (VaR) : Historical simulation, the Variance-covariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variance-covariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1-day VaR for a hypothetical portfolio through MATLAB simulations. The evaluation of the results shows that historical simulation yields the most reliable 1-day VaR for the hypothetical portfolio under extreme market conditions. Finally, this paper concludes with a suggestion for further studies : a heavy-tail distribution should be used in order to imporve the accuracy of the results for the two parametric methods used in this study.