I have been thinking very hard about properly pricing volatility. Outside of naive AR,ARCH,GARCH forecasting model which employs past data to forecast future vol, how does one "fundamentally" value volatility??? The key word here is "fundamentally".
In other worlds of insurance (health insurance, car insurance, etc.) a competent underwriter can look historically at one's driving record, health record, (past data in other words) to determine one's P(claim) & loss given claim and the entire pool's P(claim) and expected losses to determine a "fair" value to tack on for taking that risk.
So here is my question, how does one determine fundamental "fair value" for volatility of volatile securities (such as equity indicies, crude oil, gold, bonds, etc) in order to assess whether vol is rich or cheap? You might say, one starting point is to look at the past and use historical vol, however I have found this to be extremely unhelpful. The past needs to be discounted heavily in financial insurance unlike other insurance products and is a poor measure of the future. The only times I have found the imp vol to historical vol useful is in the rare occasions when historical vol exceed peoples volatility expectations which then underwriters adjusted volatility expectations upward. But this is rare and ~80% of the time implied vol is higher than historical. Black swans are as rare as they come -- you can sit there patiently waiting for one and by the time you give up on one coming is when it finally happens. Hence it's not a feasible strategy. So if we can't use historical vol what can we use to get a general idea of whether vol is rich or cheap?
I painfully ask this question because I recently learned the hard way, high implied volatility doesn't mean rich volatility. I sold vol on oil over the last several months only to get burned bad. Rising volatility DOESN'T mean rich volatility!! WTI with a vol at 20 two years ago can fundamentally have had a richer vol when it was at at a significantly lower level than than when its vol shot to 60 in the last couple of weeks.
I would appreciate any good words of help, guidance on the issue. Any past published research work on the topic you have either worked on or seen would be greatly appreciated.