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Author Topic: Volatility  (Read 857 times)
xxjs
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February 17, 2013, 04:24:44 PM
 #1

It seems the concept of volatility is not well defined metrically.

It could be over some timespan, percentage of in or out value or some volume weighed indicator. It could be moving window, and it could be defined as a quadratic filter.

We need some formula that will not be distorted if value rises significantly.

Ideas?
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February 17, 2013, 07:58:44 PM
 #2

Fourier transform with a (shaped) sliding window.
Plot an array of frequency spectra, which evolves over time (just like those "graphic equaliser" gimmicks).

Any reduction in output at a certain frequency would show that price oscillations have reduced at that particular frequency. Then you just say that a reduction in output at all frequencies signifies an overall reduction in volatility.

The only thing that comes to mind for trying it out with minimal effort is somehow importing the all-time exchange rate data into an audio program like Audacity and manipulating it in there.
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February 17, 2013, 08:03:52 PM
 #3

Sorry no need to reinvent volatility Smiley It is the standard deviation of price form the median over some period of time. So you can see one plotted here for example:

http://bitcoincharts.com/charts/mtgoxUSD#rg10ztgSzm1g10zm2g25zi1gCVolatilityzv

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xxjs
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February 17, 2013, 08:33:40 PM
 #4

Great, exactly what I wanted.
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February 17, 2013, 08:50:35 PM
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Sorry no need to reinvent volatility Smiley It is the standard deviation of price form the median over some period of time. So you can see one plotted here for example:

http://bitcoincharts.com/charts/mtgoxUSD#rg10ztgSzm1g10zm2g25zi1gCVolatilityzv

Are you sure that all those antiquated concepts of open, close, daily high, and daily low are even relevant for a system that runs 24h continuously?

According to barchart.com
Quote
The basic premise of the Accumulation/Distribution Line is that the degree of buying or selling pressure can be determined by the location of the close, relative to the high and low for the corresponding period. There is buying pressure when a stock closes in the upper half of a period's range and there is selling pressure when a stock closes in the lower half of the period's trading range.

The Chaikin Oscillator is simply the Moving Average Convergence Divergence indicator (MACD) applied to the Accumulation/Distribution Line. The formula is the difference between the 3-day exponential moving average and the 10-day exponential moving average of the Accumulation/Distribution Line. Just as the MACD-Histogram is an indicator to predict moving average crossovers in MACD, the Chaikin Oscillator is an indicator to predict changes in the Accumulation/Distribution Line.

Which sounds very nice except that when there's no such thing as "a daily trading period" -- trading is spread across multiple time zones. Cherry-picking open/close times to fit a formula is going to give you aliasing errors.
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February 17, 2013, 09:11:13 PM
 #6

Great, exactly what I wanted.
No, it isn't. This volatility index does not meet your criterion:

We need some formula that will not be distorted if value rises significantly.

The quirk of standard deviations is that they too increase with a increase in value. Indeed, because these are linear standard deviations, they assign greater volatility to upwards movements than downwards ones. A standard deviation should not be used in raw form with inherently geometric data.

Instead, volatility must be calculated on the natural logarithm of the price. Chaikin volatility is an example of a calculation that comes close, working with exponential moving averages (but giving distorted results when there is a huge change in the time period).

Sorry no need to reinvent volatility Smiley It is the standard deviation of price form the median over some period of time. So you can see one plotted here for example:

http://bitcoincharts.com/charts/mtgoxUSD#rg10ztgSzm1g10zm2g25zi1gCVolatilityzv

Are you sure that all those antiquated concepts of open, close, daily high, and daily low are even relevant for a system that runs 24h continuously?

According to barchart.com
Quote
The basic premise of the Accumulation/Distribution Line is that the degree of buying or selling pressure can be determined by the location of the close, relative to the high and low for the corresponding period. There is buying pressure when a stock closes in the upper half of a period's range and there is selling pressure when a stock closes in the lower half of the period's trading range.

The Chaikin Oscillator is simply the Moving Average Convergence Divergence indicator (MACD) applied to the Accumulation/Distribution Line. The formula is the difference between the 3-day exponential moving average and the 10-day exponential moving average of the Accumulation/Distribution Line. Just as the MACD-Histogram is an indicator to predict moving average crossovers in MACD, the Chaikin Oscillator is an indicator to predict changes in the Accumulation/Distribution Line.

Which sounds very nice except that when there's no such thing as "a daily trading period" -- trading is spread across multiple time zones. Cherry-picking open/close times to fit a formula is going to give you aliasing errors.
That's not a concern with the Chaikin, because it is averaged over so long that the close time doesn't matter much. It is a concern with daily time intervals—however, there is nothing stopping one from using a longer time interval.
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February 17, 2013, 09:27:06 PM
 #7

Here's an extremely simple indicator that relies on purely geometric data. It does much better for Bitcoin because of its huge swings.

The formula:
Code:
max/min

This is a unitless measure. Effectively, that means that it is not susceptible to variation due to price variation. This is one criterion, the other is that it is reversible. The volatility is the same no whether the price is increasing or decreasing, as long as the magnitude is equal. It does suffer for aliasing, but only if the time interval is too short. A trailing weekly measure, measured daily, suffers from little aliasing.
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