William W. Ashby Lecture Series on Value Investing

We document that the implied volatility skew of S&P 500 index puts is non-decreasing in the disaster risk and/or volatility. The puzzle is that a broad class of no-arbitrage models implies that the implied volatility skew is decreasing in the disaster risk and/or volatility. The key to the puzzle lies in recognizing that, as the disaster risk and/or volatility increase, market makers become more credit-constrained in writing puts as insurance to customers. The resulting increase in the implied volatility is more pronounced in out-of-the-money than in at-the-money puts, thereby steepening the implied volatility skew and resolving the puzzle. We show that demand pressure from customers alone cannot explain the puzzle. The constrained supply by market makers helps explain the puzzle. Several implications of the model about the customers’ net buy of puts are born out in the data.