The full abstract is here.
Title: Tradable Estimates of Historical VolatilityAbstract: There are
many estimates of historical volatility, based on time samples, price
level samples, on high and low. I define an estimate as "tradable" if
it is attainable from a static position in options a dynamic trading
of the underlying. I characterize the unbiased tradable estimates,
show that the difference of two of them is a costless dynamic strategy
and show how the daily/weekly trade performs on various time
periods.The usual estimates based on high and low are not tradable.
Surprisingly, it is not because high and low are not stopping times
but because they do not depend quadratically on the final value. I
introduce a new high and low based estimate that is tradable and
unbiased.I conclude by using the newly developed Functional Ito
Calculus to characterize the contingent claims that can be replicated
by a model free strategy of dynamically trading the stock.
They are just arbitrarily defining tradable to be a specific subset of tradable. This is just a practicality thing - one could happily set up some OTC contract on whatever they want, the same way you can walk into a bookie and set up a trade on a completely arbitrary event with them. Technically this means that anything is tradable if you can find someone to take the other side; that does not make it practical.
It's also a data thing. By stipulating that it is a static position of options and dynamic holding of the underlying, the estimator becomes something that is actually useful to people with the required data to use it - I could create the perfect model of the financial markets if i were omniscient, but it would be of no use to you (assuming you're not also omniscient).