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Yang-Zhang volatility estimator
February 12, 2016, 1:56 PM
Indicators
2 Comments
For those interested in options pricing and volatility indicator, here is one that draw recent volatility based on High, Low, Open and Close prices.
For more explanation see this paper : http://atmif.com/papers/range.pdf
//parameters
// n = 20
// averageP = 200
No = log( open ) - log( close[1] ) // normalized open
Nu = log( high ) - log( open ) // normalized high
Nd = log( low ) - log( open ) // normalized low
Nc = log( close ) - log( open ) // normalized close
Vrs = 1 / n * Summation[n]( Nu * ( Nu - Nc ) + Nd * ( Nd - Nc )) // RS volatility estimator
Noavg = 1 / n * Summation[n](No)
Vo = 1 / ( n - 1 ) * Summation[n]( SQUARE( No - Noavg ) )
Ncavg = 1 / n * Summation[n]( Nc )
Vc = 1 / ( n - 1 ) * Summation[n]( SQUARE( Nc - Ncavg ) )
k = 0.34 / ( 1.34 + ( n + 1 ) / ( n - 1 ) )
Vyangzhang = Vo + k * Vc + ( 1 - k ) * Vrs
avg = average[averageP](Vyangzhang)
return Vyangzhang, avg as "average volatiliy"
code adapted from AmiBroker
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Yan-Zhang-Volatility-estimator.itf
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I think to have annualized view of this historical volatility you will need : Vyangzhang = SQRT(Vo + k * Vc + ( 1 - k ) * Vrs) *SQRT(252)