Historical Volatility Calculation Example

Assume a 10 bar historical volatility on a daily bar chart. Also assume the days have to following closes;


Day 0: 24.5
Day 1: 25.25
Day 2: 23.0
Day 3: 21.5
Day 4: 22.0
Day 5: 24.75
Day 6: 26.0
Day 7: 26.5
Day 8: 27.5
Day 9: 26.0
Day 10: 25.5


First, divide the day’s close by the previous day’s close. Find the logarithm of this value.


    Divide Results Log Results
Day 0: 24.5    
Day 1 25.25 1.0306 .0131
Day 2: 23.0 .9109 .-.0405
Day 3: 21.5 .9348 -.0293
Day 4: 22.0 1.0233 .01
Day 5: 24.75 1.125 .0516
Day 6: 26.0 1.0505 .0214
Day 7: 26.5 1.0192 .0083
Day 8: 27.5 1.0377 .0161
Day 9: 26.0 .9455 -.0243
Day 10: 25.5 .9808 -.0084

 Next, add all of the above logarithmic values together and divide by 10 to get the logarithmic mean:


.0131 - .0405 - .0293 + .0100 + .0516 + .0214 + .0083 + .0161 - .0243 - .0084 =.018

 

.018 / 10 = .0018


Now, for each of the last 9 bars and the current bar, once again divide the bar’s close by the previous bar’s close. Find the logarithm of this value, subtract the above calculated logarithmic mean, and square this value.

 

  Log Results Subtract Value Square
       
Day 1: .0131 .0113 .000128
Day 2: -.0405 -.0423 .001789
Day 3: -.0293 .0275 .000756
Day 4: .01 .0082 .000067
Day 5: .0516 .0498 .002480
Day 6: .0214 .0196 .000384
Day 7: .0083 .0065 .000042
Day 8: .0161 .0143 .000204
Day 9: -.0243 .0225 .000501
Day 10: -.0084 .0066 .000044

Add all of the above values together, divide by 9, and get the square root of this value:


.000128 + .001789 + .000756 + .000067 + .002480 + .000384 + .000042 + .000204 + .000501 + .000044 = .006395

 

.006395 / 9 = .000711


Square root of .000711 = .026656


Multiple by 15.81139 (since it’s daily);


.026656 * 15.81139 = .421468


Finally, multiply this value by 100 to get the historical volatility:


.421468 * 100 = 42.1468