VaR and other Risk Measures

一、 Estimating Market Risk Measures

1、 Profit/Loss 

 Profit/Loss Data

 Arithmetic Return Data :

 Geometric Return Data :

The difference between the two returns is negligible when both returns aresmall, but the difference grows as the returns get bigger—which is to beexpected, as the geometric return is a log function of the arithmetic return.Since we would expect returns to be low over short periods and higher overlonger periods, the difference between the two types of return is negligible over short periods but potentially substantial over longer ones.

The parametric approach explicitly assumes a distribution for the  underlying observations.? Suppose that we wish to estimate VaR under the assumption that  P/L is normally distributed. ? Suppose that we wish to estimate VaR under the assumption that P/L is lognormal distributed.

Normal VaR  We assume that arithmetic returns are normally distributed with mean μ

and standard deviation σ. Lognormal VaR

? Assume that geometric returns are normally distributed with mean μ

and standard deviation σ. This assumption implies that the natural

logarithm of p t is normally distributed, or that p t itself is lognormally

distributed. Normally distributed geometric returns imply that the var is

lognormally distributed.

• Non-parametric Approaches

• Backtesting VaR

• VaR Mapping