Overview of VaR methodologies

VaR is distinguished from other risk-management techniques in that it attempts to
provide an explicit probabilistic description of future changes in portfolio value. It
requires that we estimate the probability distribution of the value of a financial
portfolio at some specific date in the future, termed the target date. VaR at the 1ña
confidence level is determined by the a percentile of this probability distribution.
Obviously, this estimate must be based on information that is known today, which
we term the anchor date.
Most procedures for estimating VaR are based on the concept that a given financial
portfolio can be valued in terms of a relatively small of factors, which we term risk
factors. These can be prices of traded instruments that are directly observed in the
market or derived quantities that are computed from such prices. One then constructs
a probabilistic model for the risk factors and derives the probability distribution
of the portfolio value as a consequence.
To establish a VaR methodology along these lines, we need to
1 Define the risk factors.
2 Establish a probabilistic model for the evolution of these risk factors.
3 Determine the parameters of the model from statistical data on the risk factors.
4 Establish computational procedures for obtaining the distribution of the portfolio
value from the distribution of the risk factors.
For example, the RiskMetrics methodology fits into this framework as follows:
1 The risk factors consist of FX rates, zero-coupon discount factors for specific
maturities, spot and forward commodity prices, and equity indices.
2 Returns on the risk factors are modeled as being jointly normal with zero means.
3 The probability distribution of the risk factors is characterized by a covariance
matrix, which is estimated from historical time series and provided in the Risk-
Metrics datasets.
4 The portfolio value is approximated by its first-order Taylor-series expansion in the
risk factors. Under this approximation, the portfolio value is normally distributed
under the assumed model for the risk factors.