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Some interesting threads on volatility members may be interested in the
following Fed papers
#9612 Volatility and Liquidity in the futures market
#9524 Evaluating the Predictive Accuracy of Volatility Models
#9522 Modeling Volatility Dynamics
They can be order from http://www.ny.frb.org/rmaghome/rsch_pap/
With respect to statement that Omega's standard deviation function is wrong
that statement is not entirely accurate.
Population variance is calculated the same as sample variance with the
exception that N is used rather than N - 1. When N is large (say greater
than 30) the difference is negligible. Thus, N is used as the divisor for
the variance when the data set refers to a population and n - 1 when it
refers to a sample.
The requirements of selecting a simple random sample of n elements without
replacement from a finite population of N elements are met by the following
procedure:
1. Select the first sample element by giving each of the N population
elements equal probability of being chosen (probability 1/n)
2. Select the second sample element by giving each of the remaining N - 1
population elements equal probability of being chosen (probability 1/n-1)
3. repeat this process until all n sample elements have been selected.
Thus, one can see why n-1 is used to calculate sample variance and N is used
to calculate population variance.
so the question becomes are you calculating from a sample or from a
population. The definition of an infinite population is a process its
elements consist of all the outcomes of the process if it were to operate
indefinitely under the same conditions. Now we are stuck -- Bond futures
operate indefinitely but they do not operate under the same conditions.
However, when calculating standard deviation of a financial time series the
trader not sampling randomly either. So, pick your poison when N is large
the difference is not material -- and Omega's choice is statistically and
theoretically correct.
With respect to the required number of days to annualize volatility the
annualized vol number is very sensitive to this assumption resulting in a
swing of as much as 300 bp
# of Daily Observations Number of days used for
annualizing
250
260 365
10 days
T=10 12.86%
13.11% 15.54%
T=9 13.56%
13.82% 16.38%
20days
T=20 26.39%
26.91% 31.88%
T=19 27.07%
27.61% 32.71%
Source: Handbook of fixed income securities pp417
Finally, using logs in the calculation is fine when you are dealing with
prices. However, when dealing with interest rates logs actually allow for
negative interest rates which is no likely. Thus, if you are calculating
yield Volatility you should use percent change.
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