What is volatility?
Math warning!
In this article, I'm going to introduce the concept of volatility, log return, and standard deviation, providing the mathematical background to help you gain a better understanding of these concepts. I will also introduce the four main volatility formulas to illustrate the evolution of volatility estimation: Parkinson, Garman-Klass, Roger-Satchell, and Yang-Zhang.
Math warning!
When we talk about volatility, we look at the returns rather than closing prices because returns reveal the actual magnitude and direction of the daily price changes, standardizing the measurement of price variability across time and different assets.
By definition, volatility is the annualized standard deviation of the periodic logarithmic returns.
And like this volatility basically shows us the “real velocity” of the price action indirectly giving us a picture about the liquidity at certain spot levels.
Liquidity means how easy it is to turn an asset back into cash. The higher the liquidity, the easier and more cost efficient it is to do, and vice versa.
if volatility is low, this means that the log returns are compressing as a result of high buying and selling activity at certain territories, because the interest are met there. Au contrary, when volatility is high, this means that the buyers and sellers must “look for each other”, and so the price movements expand, so does volatility.
But now, let’s dissect this definition of log returns starting with math basics…
What is logarithmic return?
Return is the profit on a trade which the trader receives from that position over a given time period.
Let’s say Vᵢ is the initial value of our capital and the end value is Vₑ
Then simple return is: