Historical Simulation is a simple, non-parametric method to assess market risk, almost not depending on assumptions about the distribution function of the underlying risk factors. Instead, one utilises market price changes for the portfolio evaluation. Only in the case of pricing of derivatives, certain model assumptions cannot be avoided.
In the simplest case, the instrument return is found by weighing the differences of market prices with the portfolio holdings. Taking absolute differences is not scale invariant and gives a distorted statistical set when the instrument price changes considerably, e.g. in the case of long time horizons. One can solve this problem by calculating shifts whose relative returns are rescaled to the current market value.
From the resulting P&L distribution common risk measures (VaR, TailVaR etc.) can be derived. However, by construction the number of available data points equals the number of periods, mostly days. Moreover, reproducibility considerations imply that one cannot choose a time frame of an arbitrarily given length in the past. Thus, the number of such data points is much smaller than in a stochastic modeling approach. Here, B&C works with concepts from Extreme Value Theory (EVT) to derive robust risk measures from the tails of the distribution function.
Historical Simulation strongly depends on the quality of the underlying market data. Since gaps in time series hardly can be accepted, they have to be quality-controlled separately. For this task, cascade shaped systems of rules have proven especially effective.
Similarly to the case of the stochastic approach, one has to ask whether the considered time frame actually is the right one to describe the quested risk information adequately. This holds particularly for the reproduction of rare extreme events. One of the advantages of Historic Simulation is that stress test not necessarily have to be performed separately. Under certain conditions, they can be integrated in the time period under consideration.
If responsibly implemented, Historical Simulation turns out to be an impressively simple method to derive well-grounded risk information, yet without begin overly dependent on the use of model assumptions or Monte-Carlo scenarios.