Technical indicators Garmin-Klass Volatility

Parkinson volatility

Before talk about Garmin-Klass volatility, it is better to understand Parkinson volatility.

Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day. The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. A large price movements could happen during the day and if only the close prices are used, it could lose a lot information. Therefore Pakinson’s volatility is considered to be more precise.

The following formula shows the calculation of Parkinson volatility, where $T$ is the number of days in the sample period, $h_t$ is the high price on day t and $l_t$ is the low price on day t.

One main drawback of this estimator is that it doesn’t take into account price movements after market close, that’s why we need to consider Garmin-Klass’s volatility estimator.

Garmin-Klass’s volatility

Garmin-Klass volatility extends Parkinson’s volatility by taking into account the opening and clossing prices. As markets are most active during the opening and closing of a trading day, it makes volatility estimation more accurate.

The following formula shows the calculation of Garming-Klass volatility, where $o_t$ is the open price on day t, $c_t$ is the close price on day t.

We will try to implement Garmin-Klass’s volatility in Python.

import pandas as pd
import sqlite3

# load S&P500 data from stored database
sp500_db = sqlite3.connect(database="sp500_data.sqlite")

df = pd.read_sql_query(sql="SELECT * FROM SP500",
                       con=sp500_db,
                       parse_dates={"Date"})
df.head()

	Date	Ticker	Adj Close	Close	High	Low	Open	Volume
0	2014-04-29	A	35.049534	38.125893	38.304722	37.174534	38.118740	4688612.0
1	2014-04-29	AAL	33.476742	35.509998	35.650002	34.970001	35.200001	8994200.0
2	2014-04-29	AAPL	18.633333	21.154642	21.285000	21.053928	21.205000	337377600.0
3	2014-04-29	ABBV	34.034985	51.369999	51.529999	50.759998	50.939999	5601300.0
4	2014-04-29	ABT	31.831518	38.540001	38.720001	38.259998	38.369999	4415600.0

# calculate Garmin-Klass volatility
import numpy as np
df['garmin_klass_vol'] = ((np.log(df['High'])-np.log(df['Low']))**2)/2 - (2*np.log(2)-1)*(np.log(df['Adj Close'])-np.log(df['Open']))**2

df.head()

	Date	Ticker	Adj Close	Close	High	Low	Open	Volume	garmin_klass_vol
0	2014-04-29	A	35.049534	38.125893	38.304722	37.174534	38.118740	4688612.0	-0.002274
1	2014-04-29	AAL	33.476742	35.509998	35.650002	34.970001	35.200001	8994200.0	-0.000788
2	2014-04-29	AAPL	18.633333	21.154642	21.285000	21.053928	21.205000	337377600.0	-0.006397
3	2014-04-29	ABBV	34.034985	51.369999	51.529999	50.759998	50.939999	5601300.0	-0.062705
4	2014-04-29	ABT	31.831518	38.540001	38.720001	38.259998	38.369999	4415600.0	-0.013411

# update the database
df.to_sql(name="SP500",
          con=sp500_db,
          if_exists="replace",
          index=True)
sp500_db.close()