Historical Simulation
Uses actual daily historical returns
It captures the abnormality of asset returns
This is the most straightforward way of calculating VAR.
All historical observations are treated equal.
Returns the percentile from the historical returns.
There is no explicit underlying model
The disadvantage is that it assumes independent returns and there is no unconditional covariance structure.
Uses historical data from that asset and assumes that the same return can re-occur at a given time in the future.
Most companies use historical data.
Advantages
Incoporates the inter risk factor correlation structures
There are no model assumptions around parameters or calibration
Disadvantages
Requires an enormous amount of historical information
Must be able to handle missing or incomplete data
How to Price:
Generate the daily historical returns
Some time series are more lognormal
Some time series are more normal
Generate the different forecasted market scenarios
Calculate the profit and loss vector
Estimate the VaR Quantile
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