Historical Simulation

Overview

Historical Simulations are a model that attempts to overcome the deficiencies of the parametric and monte carlo methods. The primary problem with these two approaches is that the modeler specifies the distribution of the assets in the portfolio and then fits the distributions to the data through a set of parameters.

Historical Simulation Theory

Many model blow ups are due to mis specification of the risk distribution. For example , many blow ups are due to modeling risk using the Gaussian distribution, which is known to understate the tail risk of most assets. Historical simulation overcomes this issue by using actual historical data to simulate possible futures.

Shortcomings

Historical Simulation Theory

Historical simulation is based on the statistical theory of resampling. Essentially, the analyst starts with a dataset representing historcial asset prices or returns. The analyst then randomly selects a date from the set of dataset and applies whatever returns occurred to the assets in their portfolio that occurred to them on that selected date.

Scaling the Time Frame