# How to calculate Parkinson's Historical Volatility

I want to calculate volatility of stock prices. I found information here, but I'm not sure if I'm doing right.

These are sample data:

Date,High,Low
2001-11-15,137.0,134.0
2001-11-16,140.0,133.0
2001-11-19,140.0,137.0
2001-11-20,140.0,136.0


And I calculate in condition n=3.

daily valiation of 2001-11-15 is:

(1 / (4 * ln(2))) * ln(137/134)^2
+ (1 / (4 * ln(2))) * ln(140/133)^2
+ (1 / (4 * ln(2))) * ln(140/137)^2


and valiation of 2001-11-16 is:

(1 / (4 * ln(2))) * ln(140/133)^2
+ (1 / (4 * ln(2))) * ln(140/137)^2
+ (1 / (4 * ln(2))) * ln(140/136)^2


Is this calculation right? If wrong, where can I find example of calculation of volatility with some data? What I could find were all only formulars without numbers.

I believe it is partially correct. The summation term is missing $\frac{1}{n}$ and I assume you left out the square root intentionally. Also, I believe since it is historical volatility, you should be using dates going backward and not forward.

ivolatility.com also describes classic historical volatility using the same summation range as Parkinson's volatility. This other site also describes the two historical volatility metrics using the same summation range. So both the classic estimator and the Parkinson estimator have their summation over the same period of time. They just sum over (very) different terms.

Classic historical volatility is carefully described here and here. They both use historical dates and not dates going forward. So the Parkinson volatility should be

$$ParkinsonVolatility_{2001-11-19} = \sqrt{\frac{\frac{1}{4 * ln(2)} * (ln\frac{140}{137})^2 + \frac{1}{4 * ln(2)} * (ln\frac{140}{133})^2 + \frac{1}{4 * ln(2)} * (ln\frac{137}{134})^2}{3}}$$