# How to apply decay factor in the volatility calculation for 1 asset?

I read somewhere that the decay factor is (1-lamba)*lamba^t where t is first return, second return, third return, ...

I also found this formula which I have difficulty to understand:

How do I calculate the volatility of my asset taking into account my 0.97 decay factor? I have the time series of daily prices.

Normally to get volatility I would get the average daily return, then calculate the variance by summing all the (return-average return)^2 and dividing by N.

I would then square the variance and multiply by square(25) to have a volatility for a period of 1 month.

At what stage am I supposed to incorporate the decay factor?

Effectively, you take your series of prices and transform those to returns as you would do in your standard approach, as well.

step   return date  weight
1      2020-03-26   0.97
2      2020-03-25   0.97 * 0.97
3      2020-03-24   0.97 * 0.97 * 0.97
...
K      T-K+1        097^K


For $$K$$ sufficiently large, the sum of the weights $$\sum_i \lambda^i$$ will converge to $$\frac{1}{1-\lambda}$$, hence the prefactor in your formula.

In order to calculate your volatility, you do not sum the squared returns and divide by $$N$$, as you would do normally, but you compute the weighted sum of your squared returns, normalised by $$1-\lambda$$. You may then calculate the square root to arrive at your $$\sigma_t$$.