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 Garman-Klass Volatility
Issued on September 11 2011 par Strategies-options.com
First Close to close, then Highs and lows. Next both with opening price added !
First we have seen the close to close volatility ( Volatility : Trading Formulae ) . We then have seen Parkinson's one ( Parkinson Volatility ). The obvious next step is to link both of them. With another data.
I - A simple fact to take into account The previous formulae are correct as far as the market is a continuous one. Forex seems to be the right candidate. But even with forex trading, there are some gaps. It's straightforward to take into account this feature by adding another data : the opening price. That's Garman-Klass Volatility. II - A formula, a better efficiency The next formula is 7.4 more efficient than close to close volatility, that is, 7.4 less data are needed to reach the same accuracy. The formula : For n days, Garman-Klass variance is σ²(GK) = ( 1/n ) . ( ∑ [0.511 . ( ln( Hi/Li) )² - ( 0.019 . ln( Ci/Oi ) . ln( HiLi/(Oi²) ) ) – (2 .ln( Hi/Oi ) . ln( Li/Oi ) ) ] ) With, Oi opening price for the ith day Ci closing price for the ith day Hi Highest price for the ith day Li Lowest price for the ith day Ln is the natural logarithm Hence, Garman-Klass Volatility is : σ (GK) = √ [ 252 . ( 1/n) . ( ∑ [0.511 . ( ln (Hi/Li))² - ( 0.019 . ln(Ci/Oi) . ln(HiLi/(Oi²))) – (2 .ln(Hi/Oi) . ln (Li/Oi))] ) ] If there are 252 trading days to annualize that number. III - Example Using Open, High, Low and Close prices on CAC 40 Index, it leads :  Next : Implied Volatility Previous : Parkinson Volatility Related Articles : - Garman Klass Volatility link : On the Estimation of Security Price Volatility from Historical Data - The Garman-Klass volatility estimator revisited - Modelling Volatility Using High, Low, Open and Closing Prices: Evidence from Four S&P Indices OPTIONS 101 - INDEX OPTIONS 101 - CHAPTER I OPTIONS 101 - CHAPTER II OPTIONS 101 - CHAPTER III OPTIONS 101 - CHAPTER IV OPTIONS 101 - CHAPTER V OPTIONS 101 - CHAPTER VI Strategies-options.com |
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