Extracting Disaster from Index Option Prices

Does the “overpricing” of out-of-the-money (OTM) stock index put options imply an investor estimate of the likelihood and size of economic disasters and stock market crashes? In his June 2008 paper entitled “How Bad Will the Potential Economic Disasters Be? Evidences From S&P 500 Index Options Data”, Du Du estimates the the frequency and magnitude of U.S. economic disasters as implied by S&P 500 index option data within a model involving rare sharp drops in consumption and consumption habit formation. In his model, consumption drops induce stock market crashes via: (1) commensurate declines in dividends, and (2) elevated investor risk aversion. Using S&P 500 index option data for the period 4/4/88-6/30/05 and contemporaneous economic data, he concludes that:

• Differences in price between deep OTM and at-the-money index put options provide important information about investor expectations of disaster.
• Empirical data indicates that investors expect U.S. economic disasters to strike every 36-64 years in the form of 13.5%-17.6% contractions in consumption, which induce 36%-56% crashes in the stock market.
• These indications are broadly in line with the 10% annual consumption contraction during the Great Depression.

In summary, pricing of out-of-the-money put options for the S&P 500 index indicates that investors expect 50% stock market crashes every 50 years.