Choosing the Correct Periods for Yang-Zhang Volatility
Choosing the Correct Periods for Yang-Zhang Volatility
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lolo · External communityPost link
External question — Quantitative Finance Stack Exchange
Author: lolo
Original post: https://quant.stackexchange.com/questions/40963
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
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I am implementing the formula for YZ Volatility using
this link
.
I am testing it on hourly Forex charts and I'm getting some strange numbers. Taking the 14 day YZ volatility using
Z
as
252 * 24
(for hourly) I get numbers like
0.280535
. Backing it off to
252
I get numbers like
0.0280535
. In reality, it should be
near
the naive standard deviation
0.002x...
.
I'd like to confirm my assumptions on the periods are correct.
In the paper
Z
is described as the number of closing prices in a year. For daily data, I would assume this would be
252
. Since I am doing this on hourly data my assumption is that this would be
252 * 24
. Is this correct? The strangest thing is that the volatility seems correct, except for the fact it's two decimal points too far to the left.
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Alex C · External communityPost link
External answer — Quantitative Finance Stack Exchange
Author: Alex C
Original post: https://quant.stackexchange.com/a/40964
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
Adaptation: HTML converted to plain text; contact email addresses removed.
Let's talk about time units.
The "result time unit" is the time in which you want the final result to be expressed. For example if you want "yearly volatility" or volatility per year then the RTU is "1 year"
The "basic time unit" is the time between successive closing prices that you observe. For Yang the BTU is one day, but for you (since you have decided to use hourly data) the BTU is "1 hour".
Now the numbers $n$ and $Z$. $n$ is the number of values in the summation ($\sum_{i=1}^n$), it is also the number of basic time intervals you have observed. For example if you are looking at the last 14 trading days using hourly prices then $n=14*24$. $Z$ is the number of BTUs in one RTU. So for computing yearly volatility from hourly data $Z=252*24$.
HTH
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Quoted from Forex.com.bd-Editorial External answer — Quantitative Finance Stack Exchange Author: Alex C Source score (net votes, not local likes): 1 Original post: https://quant.stackexchange.com/a/40964 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Let's talk about time units. The "result time unit" is the time in which you want the final result to be expressed. For example if you want "yearly volatility" or volatility per year then the RTU is "1 year" The "basic time unit" is the time between successive closing prices that you observe. For Yang the BTU is one day, but for you (since you have decided to use hourly data) the BTU is "1 hour". Now the numbers $n$ and $Z$. $n$ is the number of values in the summation ($\sum_{i=1}^n$), it is also the number of basic time intervals you have observed. For example if you are looking at the last 14 trading days using hourly prices then $n=14*24$. $Z$ is the number of BTUs in one RTU. So for computing yearly volatility from hourly data $Z=252*24$. HTH
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