Overview
Historical Simulations Value at Risk models were built as an attempt to overcome the deficiencies of the parametric and monte carlo methods.
The primary problem with other approaches is that the modeler specifies the statistical distribution of the assets in the portfolio and then fits the distributions to the data through a set of parameters. However, the analyst cannot know the actual distribution, and assumptions about the tail behaviour of whatever distribtution is chosen can have a dramatic effect on the results.
The historical simulation method bypasses this challenge by sampling from the history of the assets in the portfolio, and applying the samples to todays prices. This technique is essentially the method of bootstrap applied to asset prices. (see also sampling)
Algorithm
The historical stimulation of asset prices needs to start with the prices given at the beginning of the simulation, which is typically taken to be the asset prices today. Then, changes to the asset prices are sampled from the historical data, and applied the current prices. There are essentially two ways to sample the history.
- Take the historical data, and compute return differences in the prices of each asset over the period
specified in the VAR measure. For example, if the VAR is taken to be over a year time frame, then
compute yearly differences for each asset in the portfolio in the historical data, and then sample from
these differences.
While theoreitcally sound, the problem with this method is that for time frames of a reasonable size, the resulting dataset will be small, and therefore not statistically relevant. - As an alternative, compute daily return differences to the historical prices. Randomly sample a set of
returns from the history and then apply each return to todays prices. This method overcomes the issue of
data size, however, it throws away information, such as correlation from one daily return to the next,
that may be critical in risk measure.
As an alternative, the VAR can be computed on a daily basis, and then scaled. (see scaling VAR)