The volatility

Financial markets are constantly evolving trough different cycles and trends in response to macroeconomic and microeconomic factors. In this sense, it is important to be able to measure the potential change in value of an asset  to invest in the numerous financial supports such as options which are priced with respect to the anticipated value variations of their underlying asset on a determined period of time.

What is the volatility ?

The volatility is the indicator by default of of investor to try to catch the potential range of variation of any assets on the market. More specifically it can be defined as a statistical measure of the dispersion of returns for a given security or market index and we commonly consider that the higher the volatility, the riskier the security.

How do we measure the volatility ?

Here we have different possibilities that we are going to explore one by one in order to have a broader view of this indicator and be able to choose depending on the scenario the best way to compute the volatility indicator.

1^st Method : The empirical volatility

This volatility mainly used in the econometric litterature is usually defined as the standard deviation of the daily return of an asset and express as follows :

with :

r_m : the mean value of the returns computed on [1,t]

r ( t ) : the return on [t - 1, t]

2^nd Method : The trading volatility

In practice, we cannot use the empirical trading volatility because as we can see if the mean return is equal to the daily return then the volatility is null. This is why on the market investors prefer to use a volatility indicator non-centered on the mean express as follows :

with :

r (t)  :  the return on the period [t-1,t]

Note : the two prior expression of the volatility are not annualized but to do so we can easily see that we will only have to multiply by the number of day in a year.

Example :

3^rd Method : The Parkinson volatility

The Parkinson volatility can be interesting for volatile assets as it uses instead of the closing price, the High/Low of the day in order to take into account the intraday volatility of the stock price  :

with :

n : the number of days

Hi : the high of the day

Li : the low of the day

(note : Here we consider a year of 252 business day)

4^th Method : The Garman Klass volatility

Here, besides taking into account the intraday volatility we also take into account the possible gaps in the price asset in order to be as close as possible of the asset price behavior :

with :

Oi : the opening price on day i

Ci : the closing price on day i

Hi : the high on day i

Li : the low on day i

Note: this indicator is usually approximately 7 times more accurate than the empirical volatility.

That is all for our presentation of the notion of volatility.