There are two common methods for calculating the market risk value at risk under Basel II: the historical simulation approach and the model-building approach.
Historical simulation is the most commonly used approach. We use the day-to-day changes in the historical values of market variables to calculate the probability distribution fo the changes in the value of the current portfolio between today and tomorrow. More advanced methods for historical simulation includes weighing the estimate towards more recent observations.
The model-building approach involves assuming a model for the joint distribution of changes in market variables and using historical data to estimate the model parameters. This approach is most commonly used for portfolios that consists of both long and short positions in stocks, bonds, commodities and other products. The mean and standard deviation of a portfolio is calculated from the distribution of the underlying assets returns and the correlation between those returns.
The model-building approach is most effective if we can assume that the distribution of the underlying assets is multivariate normal. Relaxing this assumptions makes this approach much more challenging.
Model building vs. historical simulation
The advantage of the model building approach is that results can be produced quickly. It is also easy to use together with volatility and correlation updating procedures. The biggest drawback of the model building approach is that it assumes a multivariate normal distribution. We must rely on the central limit theorem applies to the data.
The advantage of the historical simulation approach is that the joint probability distribution of the market variables is determined by historical data. It is also easier to handle interest rates in a historical simulation. Historical simulation is however computationally slow.
The model building approach is most often used for investment portfolios and not so commonly used to calculate VaR.
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