This paper outlines the steps of the three common approaches to calculating VaR and discusses some important issues about VaR as a risk measure, including its limitations. Monte Carlo simulation and historical simulation are applied to the three hypothetical portfolios which are constructed to have increasing complexity. In Monte Carlo simulation, two time horizons, one day and ten days, and simulation runs of 10,000 times are used. Because of the limited availability of data, however, 1,000 runs of simulation over one-day time horizon are utilized in historical simulation. Besides, delta approximation and delta-gamma approximation are also used to approximate the VaR estimates to avoid the complexity of computation. Log-normal models and geometric Brownian motion whose drift term is set to zero are assumed to forecast the future possible values of different market factors under consideration. Moreover, the program with explanations for calculating VaR using Monte Carlo simulation is made public for the interested reader to run in order to have deeper understanding about the approach.
Taiwan Banking and Finance Quarterly, Vol.2, No.4, pp.89-109 台灣金融財務季刊