This method returns the estimate of the volatility for the ith day made at the end of the previous (i-1)th day, using an estimate of the volatility on the (i-1)th day according to the EWMA model with respect to changes in the market variable.
This constant between one and zero, is the ratio between the ith weight and the (i-1)th weight. The smaller the value used the more sensitive the model is to resent changes in the volatility.
I_1thDayEst
This is the previous reading or estimate of the volatility on the (i-1)th day.
Endi_1thDay
The market variable (for example, asset price) at the close of the (i-1)th day.
Starti_1thDay
The market variable (for example, asset price) at the start of the (i-1)th day.
Remarks
The EWMA
model is a special case of the ARCH model, where the weights assigned to the
historical volatility measure decreases by a constant factor.
Remarks:
Updating Formulae - this method updates the volatility estimate for the (i-1)th
day with the volatility estimate for the ith day. This method can be inductively
applied in order to derive the volatility on the ith day from the volatility on the
0th day. This method ewmaVolatilityEstimateInduction is an implementation
of this.
Weight Ratio - J.P.Morgan's Riskmetrics group found that across a range of market
variables, by taking weightRatio = 0.94, the forecasts of the volatility rate came
closest to the realized volatility.
Market Variable - the volatility can to measured with respect to any market variable.
The most common used market variable will be asset price in which case this method will
estimate the volatility of the price.
Excel Remarks
The full name of this function inside Excel is Port_Volatility_EwmaVolEst.