Put protection can be expensive - a problem of supply constraint

If there is a crisis or just expectations of a downside event, investors want to buy put protection. For many, this is the main purpose of the options market, but there is a cost with buying this protection in the form skew. There is significant skew for out of the money puts that transcends no arbitrage conditions. With jump risk and stochastic volatility, there can be skew that is related to these two factors; however, in realty, skew seems to be independent or at least less dependent on jump risk and changing volatility.

This skew behavior is a puzzle within the structure of a no arbitrage model, but can be explained by simple demand and supply between put buyers and the willingness of market-makers to write put options. As the demand for puts increases, there has to be sellers on the other side of the transaction, but if there are credit constraints on option writers, there will not be enough capital to match the demand. Consequently, the price of puts have to rise relative to at the money options. Hence, there is skew.

This supply and demand story is nicely developed by George Constantinides and Lei Lan in their paper, "The supply and demand of S&P 500 put options." The authors find that skew is a non-decreasing function of the disaster index and risk neutral variance. The disaster index in the difference between the integrated measure of implied volatility minus the VIX index squared, and the risk neutral variance is the VIX index squared. The disaster index can be thought of a measure of jump risk through looking at risk reversals. When disaster risk and variance increase, there is more put buying but writers may be constrained by the higher volatility which causes a imbalance that can only be corrected by higher premiums. Skew increases when border-dealers have a high liability to asset ratio and the more likely to be credit constrained. Demand pressure is not enough to have increased skew. Writers have to be constrained and need more return to undertake market-making.

These results tell us that pricing for OTM put options can get more expensive in a crisis and investors  need to pay-up for their hedges. When the crisis comes, it will be too late to buy cheap insurance. But, we have already figured that out. Insurance is expensive when the house is on fire.