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Let x be the closeBid price of EUR/USD, sampled every 5 minutes during year 2015 (historical data). This is the variation (is it correct to call it 5-minutes returns?) for each 5-minutes period:

r = x[1:] / x[:-1] - 1

What's the formula to have the (moving) volatility over 1 year?

I tried this way:

rolling_stddev(r, 288*10)     # 10 days, since 288 periods of 5 minutes in 1 day

The results is:

enter image description here

Is it a correct measure of volatility? (i.e. standard deviation of the returns)

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First I thought about voting to close this question as it deals with Matlab synthax a lot. I ignore the Matlab stuff.

You have 5-minutes data. So an estmator of volatility over any sample of size $N$ (e.g. 100) will be an estimator of the vol of your 5-min returns. Usually volatility is quotes as "per annum" or "pa". This means that using the square root of time rule you can multiply your estimate by the number of 5-minute intervals in a year. Thus if you want to quote vola pa then $$ T = 12*24*260 = 288*260 $$ assuming 260 banking days and you multiply your estimate by $\sqrt{T}$. If you do the calculation for 10 days then $T=288*10$.

The $T$, the holding period, is independent from the number of returns that you use in order to estimate the 5-minutes vol.

Doing the things rolling does not change anything of the things above. You just push a window forward by 1 return each time.

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  • $\begingroup$ This assumes sampling for the entire day (12 * 24). Would that be more accurate to do it just for the trading hours? $\endgroup$ – SmallChess Jan 8 '16 at 0:40
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It's better to use an exponentially weighted moving average.

There's a nice tutorial video by the Bionic Turtle here

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  • $\begingroup$ Ok for EMA, right. But more generally, is it mostly correct (to use standard deviation of returns) ? Would you multiply by some constant? $\endgroup$ – Basj Jan 7 '16 at 16:42

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