FR H-Volatility - page 23

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kamal:
Prival:
Could you elaborate on this, please, it is not clear if the lull is about the price, then we will not come out of the silence, or something else is going on here. It seemed to me that the lull is followed by a strong movement. Thank you.

You keep looking at the market deterministically and that's not very right. Yes, after a lull a lull is more likely, but that does not mean that volatility cannot suddenly spike. It is just that periods of low and high volatility are indeed distinguishable, both on small timeframes and globally (for example, we have now come out of a multi-year low volatility cycle and entered an equally multi-year high volatility cycle, see the VIX chart).

I think I understand if volatility is the number of deals per time unit. Then let me give you some more insight. In your opinion, are these processes (price and volatility) correlated? Is there an anticipation at the beginning of movement relative to each other? That is, what begins to change earlier volatility or price?

Also, what is a VIX chart, I've just rarely communicated with traders. I do not masters many terms you might be familiar with.

 
I think I understand if volatility is the number of transactions per time unit, then let's go over it one more time. In your opinion, are these processes (price and volatility) correlated? Is there an anticipation at the beginning of movement relative to each other? I.e. what begins to change earlier volatility or price?
Well, volatility is volatility, implied volatility of options if you like. Although in forex it seems to trade on its own as a number. In general, I really don't understand why the grief-dz don't introduce forex options, as an extension of the range of services. At the same time they will improve their terminology, there should be at least some use of Forex :)))
Also, what is a VIX chart, I've just rarely talked to traders before. And I don't know a lot of terms that you understand

VIX is a Chicago stock exchange volatility index, traditionally used to measure global market volatility. h ttp://finance.yahoo.com/q/bc?s=%5EVIX&t=my&l=on&z=m&q=l&c=

And I'm not a trader, I'm more of a quant.

 
kamal:

Regarding the max deviation: in general it is non-trivial. So what are our assumptions, are the indicator values at different moments independent? or are they sums of independent values? or neither? In the general case there is no single algorithm, we must look specifically.


The values certainly cannot be considered independent. The dependence between them must be as strong as between price values. I can hardly say anything more about it. However, as a first approximation, it's important for me to understand how the SP distribution can be used to solve this problem. At least under the assumption of independence of the values.

One variant of this problem can be formulated for a price series, namely - a tick series. It is the equibrium variant of bar plotting. But I am interested not in the bar plotting but in the price change per N ticks, i.e. in this case it is the sum of increments. Can we calculate the distribution of this sum if there is a distribution for ticks ? How can the distribution of this sum be used to calculate the MO of its maximum ? If it is possible, of course.

As far as I know, VIX is a stock index and is based on option prices. Can it be used in forex, are currency options available as well ? Or is it already in use ? The classic way to measure volatility in forex is the variance. But of course this can hardly be called an adequate measure. You write about distinguishable periods of low and high volatility. What do you use as its measure (in forex)?

 
Yurixx:
kamal:

Regarding the max deviation: in general it is non-trivial. So what are our assumptions, are the indicator values at different moments independent? or are they sums of independent values? or neither? In the general case there is no single algorithm, we must look specifically.


The values definitely cannot be considered independent. The correlation between them must be assumed to be as strong as between price values. I can hardly say much more about this. However, as a first approximation, it's important for me to understand how the SP distribution can be used to solve this problem. At least under the assumption of independence of the values.

One variant of this problem can be formulated for a price series, namely - a tick series. It is the equibrium variant of bar plotting. But I am interested not in the bar plotting but in the price change per N ticks, i.e. in this case it is the sum of increments. Can we calculate the distribution of this sum if there is a distribution for ticks? How can the distribution of this sum be used to calculate the MO of its maximum ? If it is possible, of course.

As far as I know, VIX is a stock index and is based on option prices. Can it be used in forex, are currency options available as well ? Or is it already in use ? The classic way to measure volatility in forex is the variance. But of course this can hardly be called an adequate measure. You write about distinguishable periods of low and high volatility. What do you use as its measure (in forex) ?

1) Well, may be the increments at least be independent and equally distributed? Otherwise I do not understand why there is only one distribution function (as we discussed before, for a process in general it is necessary to specify a complex construct in order to specify it completely).

And ticks behave even more accurately as a BM than just price, so root. Generally in the case of zero MO and independent increments all the time the growth will be of the order of the root.

2) Yes, you are absolutely right about the calculation methodology. Of course you can do exactly the same on forex, and moreover options are actually quoted in volatility by decent dealers. The variance of returns is a theoretical estimate (the so-called historical volatility), when the volatility is traded (directly or via options) the implied volatility) its importance goes down.

 
kamal писал (а): Mathematically: volatility is persistent.
But Peters (actually Peters, but that's how it is) in "Fractal Analysis of Financial Markets" says that it is, on the contrary, antipersistent (p. 146 and further in the Russian translation). That is, that the H for it is less than 0.5.
 
Mathemat:
kamal wrote (a): Mathematically: volatility is persistent.
And Peters (actually Peters, but that's how it is) says in "Fractal analysis of financial markets" that on the contrary, she is antipersistent (p. 146 and further in Russian translation). That is, that the H for it is less than 0.5.

Look at the 5 year chart of the VIX. In terms of local dynamics, it certainly goes back and forth a lot. Volatility is very volatile.

But in a global sense the trends can be seen very well. Very smooth trends. By the way, I see that in 2007 a new global trend is up. It just confirms, that American economy, stock market and dollar have hard times ahead, and it is not for one year.

 
kamal:

1) at least make the increments independent and equally distributed, otherwise I don't understand why there is only one distribution function (as we discussed before for a process in general you have to specify a complex construct in order to set it completely).

And ticks behave even more accurately as a BM than a simple price, so root. Generally in the case of zero MO and independent increments all the time the growth will be of the order of the root.


OK, let them be independent and equally distributed, let them be Brownian motion. I want to construct equal tick volume bars for the ticks in the Brownian motion model. The tick volume varies in proportion to the root of time. But how will the range of tick bars change, if each tick contains N ticks ?

The MO of the process is 0. The MO of these equitic bars will also be 0. However, the maximal bar size, i.e. High-Low, is not equal to 0 and must increase with time. How ? Furthermore, this size depends on N. How ? How to calculate it in this simple model ?

 
Yura, if possible, take the logarithm of the index increments (keeping the sign of the increment) and sum up the resulting series. It is interesting to look at the result and compare it with the original BP.
 
Neutron:
Yura, if possible, take the logarithm of the index increments (with the sign of the increment retained) and summarize the resulting series. It is interesting to look at the result and compare with the original BP.


Hi Sergei !

Give us a little more detail. What is the index ? Is the incremental modulus |Idx(x)-Idx(x-1)| ? Or maybe it's a relative value ? What is the data array, over what period ?

As far as I understand, you want to replace the first differences by their logarithms, and the resulting series to integrate ?

 
Suddenly I thought - there is a simple test of the concept of operating time. We need to build a spread-duration diagram for equal-tailed bars, the presence of a "trend" on it will mean that there are problems with the concept.
As for the lack of tails, the statistics in kamal's picture is obviously insufficient for such a subtle thing as fat tails.

P.S. Or chart returns - duration.
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