Options: Notes and Literature

I see optionality everywhere…almost. Actually, there are a number of widely held beliefs that confuse optionality with the convex strategies that replicate optionality. In other cases, any low probability, high returns payoff is deemed an option. But even though many see options where there are none, there are many ‘real options’ that don't much attention.

There are various reasons why there should be a risk premium for selling volatility. A non-rigorous motivation for why this should be, goes like this: An insurance policy is an option and selling insurance is a business. It should be a profitable business, as it would be quite odd for an unprofitable business to continue for so long. But then insurance companies also fail. And wrong beliefs can exist indefinitely, or be reborn again.

There is a difference between insurance and, say, equity options. Unlike equity options, hedging insurance is often not possible. But perfect replication of options is not possible either. If these hedged positions perform poorly in the bad states when certainty is desirable, that alone would explain a risk premium.

As with other risk premia, it is interesting to consider any micro-foundations of supply and demand. There is no reason the volatility risk premium should be static. There may be some natural sellers of this type of risk premia, and this supply, if any, is supplemented by those in the business of getting paid for bearing risk. There are times when supply is abundant and times when it is scarce. Identifying shocks to the supply curve seems, to me, a good use of resources for those looking to dynamically allocate to this risk premium. It is better, ceteris paribus, to bear this risk when it is unpopular to do so, when supply is scarce.

Delta‐Hedged Gains and the Negative Market Volatility Risk Premium

Demand-Based Option Pricing

Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options