what are some interesting/counterintuitive things you have learned trading options?
- Thread starter thepolarbear
- Start date
It's not calculus. The common formula is a measure of variance that falls in the domain of bayesian statistics.
Yes, for the modified formula, n is trading periods. The link provides a description of each variable. They use logs, but I don't think you have to.
You should be able to recognize and appreciate the point of this as a conceptual exercise without making the effort to program it in Excel. The next question then becomes, what is the best way to measure volatility from an option trader's perspective that avoids the deficiencies of the commonly used approach. That topic deserves a thread of its own, for another day.
It was the notation I was struggling with, ie the sigma n , t=1 stuff.
I'll test it with and without logs and see if there is much of a difference, as well as how significantly the result differs from the usual HV formula.
Thanks for the link and the helping hand.
i just took statistics.. and i asked specifically why we n-1 in the denominator when finding stardard dev.. remember.. historic vol is just a measure of past volatility.. or standard dev..
if we take a population standard dev we wouldn't use n-1 because there are no degrees of freedom..
degrees of freedom is like allowing for the unknown.. because here when we find HV we are using a sample of the population.. not the entire population.. we can never know the entire population of stock returns.
so the more trials we have.. trials being "n" variable here.. the less relevant that one degree of freedom are and the more we can rely on the distribution.. as you scale down in trial sizes your error rate goes up naturally .. so n-1 or that space that you left open to vary called the one degree of freedom scales up in relevance in relation to the sample size getting smaller and smaller..
Where:
Vol = Realized volatility
252 = a constant representing the approximate number of trading days in a year
t = a counter representing each trading day
n = number of trading days in the measurement time frame
Rt = continuously compounded daily returns as calculated by the formula:
Where:
Ln = natural logarithm
Pt = Underlying Reference Price (âclosing priceâ) at day t
Ptâ1 = Underlying Reference Price at day immediately preceding day
you have to understand what the natural log is doing...
first you have to understand the constant e... its very simple..
http://en.wikipedia.org/wiki/Natural_logarithm
http://en.wikipedia.org/wiki/E_(mathematical_constant)
its the constant multiplier that you approach when you compound 100 percent interest to near infinitismally small amounts of time..
IE 100 percent a year on 100 dollars is 200...
100 percent a year compounded every 6 months
is 100*1.5=150 + 150*1.5 = 225
and if you compound in quarters you get a higher value..
and in eights you get a higher number.. untill you approach 2.71828.... which is "e"
"e" which is the result of continuous compounding.
think of it as the multiplier if you compounded every possible moment...
Vol = Realized volatility
252 = a constant representing the approximate number of trading days in a year
t = a counter representing each trading day
n = number of trading days in the measurement time frame
Rt = continuously compounded daily returns as calculated by the formula:
Where:
Ln = natural logarithm
Pt = Underlying Reference Price (âclosing priceâ) at day t
Ptâ1 = Underlying Reference Price at day immediately preceding day
you have to understand what the natural log is doing...
first you have to understand the constant e... its very simple..
http://en.wikipedia.org/wiki/Natural_logarithm
http://en.wikipedia.org/wiki/E_(mathematical_constant)
its the constant multiplier that you approach when you compound 100 percent interest to near infinitismally small amounts of time..
IE 100 percent a year on 100 dollars is 200...
100 percent a year compounded every 6 months
is 100*1.5=150 + 150*1.5 = 225
and if you compound in quarters you get a higher value..
and in eights you get a higher number.. untill you approach 2.71828.... which is "e"
"e" which is the result of continuous compounding.
think of it as the multiplier if you compounded every possible moment...
So you are saying if we take every single days data for say AAPL since the IPO we can use n, but if we are limiting our sample size to 1 year then it should be n-1?
well i would presume.. but thats if you define your population as being only the historic returns from this point in time..
but there is a problem with aggregating large amounts of historic data into a HV calculation... the more data.. the more you smooth the results... so think about this... if you have aggregated the entire history of stock returns in your HV calculation how relevant do you think scaling it to one week would be? with this example you can see how things start to get skewed..
when you aggregate vol you smooth.. when you scale from that aggregated vol number your getting a scaled down version of that smoothed aggregate.. you then are over estimating mean volatilty and under estimating larger moves..
go into hoadley.. use a 1 year calculation for historic.. it shows a graph... ..then go to three years.. look at how all the spikes have been smoothed right out.. its the problem with trying to over optimize/normalize your moves over time..
volatility has particulars to its behavior better represented in a weighted rating with more relevance put on the near term and the clusters... Garch
Have you tested the GARCH in Hoadley?
Do you run any comparisons between GARCH forecast and realised vol?
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=299502