Why are there so many different ways of calculating historical volatility

Question

There appears to be several ways of calculating volatility:

1. Price volatility (of which there are several variants):

   • close to close
   • high low range
   • average of open, high, low and close

2. Log returns volatility

My question(s) are:

a). Why are there so many different ways of calculating volatility (since the method used sometimes changes the numbers dramatically)?

b). When is a particular method preferred?

Answer 1

The question barely fits the Q&A format.

Volatility is something which is quite abstract.

Basically the type of volatility you use depends on the model you chose to implement.

If you model asset prices, you will use price volatility.

If you model return prices, you will use returns volatility.

High-low price range can be used as a proxy for the volatility, but it's pretty unsophisticated.

In short, there is no real preferred method, the way you compute volatility depends on the model you use.