# Parkinson's volatility

Parkinson's volatility is similar to the weighted average with the difference that we only take into account the maximum and minimum prices of a financial asset at a given moment in time.

In other words, Parkinson's volatility is a modification of the weighted historical volatility taking into account the maximum and minimum trading prices.

Parkinson's volatility is born as a critique of weighted historical volatility because it only takes into account closing prices. So, this new measure defends that the historical maximum and minimum prices contain relevant information for the future in the short and medium term. The four price modalities (opening, closing, maximum and minimum) are much more informative together than individually depending on the operation that we are carrying out.

## Parkinson's volatility formula

Maximot: is the observation *t*sample maximum.

Minimum: is the observation* t* sample minimum.

Aperturat: it is the observation *t*opening of the sample.

Cierret: is the observation *t*closing of the sample.

ln: natural logarithm.

This form is the most used for calculating historical volatilities weighted through maximum and minimum prices.

## Transformations

- Incorporation of closing, maximum and minimum prices:

- Incorporation of closing, opening, maximum and minimum prices:

Unlike conventional weighted historical volatility, Parkinson's volatility already incorporates continuous variations (logarithms) in its calculation.

## Practical example

We assume that we want to calculate the daily Parkinson's volatility of the price of *AlpineSki*for four days.

### Procedure

We download the four price modalities: opening, maximum, minimum and closing of the share.

So, we calculate the volatility of the four trading days:

Volatility of the four trading days:

#### Parkinson's volatility: closing prices, highs and lows

Calculation of volatility with the closing prices, highs and lows of the four trading days:

#### Parkinson's volatility: closing, opening, high and low prices

Calculation of volatility with the closing, opening, maximum and minimum prices of the four trading days:

## Interpretation

The volatilities of the four trading days are:

- Parkinson's volatility = 16.41%
- Closing prices, highs and lows (Parkinson's volatility) = 14.90%
- Closing, opening, maximum and minimum prices (Parkinson's volatility) = 9.28%.

In conclusion, incorporating the opening, maximum and minimum prices depends on the nature of the financial asset and our investment strategy. So, if we are carrying out a daily operation, we will be interested in controlling all the information available. On the other hand, if we are more in the medium term, the opening will be less relevant unless we do some operation that specific day. In the same way, we can have the maximums and minimums as a reference to draw a trading channel and know the maximum historical variability of the stock.

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