What Makes a Realized Volatility Estimate Tradable
Summary
The document explains a practical definition of a tradable historical volatility estimate: one that can be replicated using a static options position and dynamic trading in the underlying. This restriction makes the estimate implementable from market instruments and data, rather than merely labeling any bespoke payoff as tradable.
It summarizes a paper’s distinction between estimators based on sampled prices and those based on daily highs and lows. The cited abstract says conventional high-low estimates do not meet the replication criterion because their dependence on the final value is unsuitable, while a newly constructed high-low estimator is described as both tradable and unbiased. The discussion also notes that differences between unbiased tradable estimates correspond to costless dynamic strategies. No derivation or empirical performance evidence is provided here, so the explanation is conceptual and limited to the abstract and a brief interpretation.
Key ideas
- Tradability is defined by replication with static options and dynamic underlying exposure.
- An estimator’s practical usefulness depends on whether the required prices and instruments are observable and accessible.
- The cited work reports that usual high-low volatility estimators are not tradable under this definition.
- A new high-low estimator is described as tradable and unbiased, but its construction is not shown.
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Full text
# What makes a realized vol estimate "tradeable"? # What makes a realized vol estimate "tradeable"? I'm trying to understand what makes a realized volatility estimate tradeable. Quoting from an abstract `"I define an estimate as "tradable" if it is attainable from a static position in options a dynamic trading of the underlying."` An example of a tradeable estimate is giving by this presentation here http://www.cboe.com/rmc/2015/CBOE-Bruno-2015.pdf I do not understand what makes this tradable. ## Answer by will (score 1) https://quant.stackexchange.com/a/34335 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).
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