In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...

The 1987 market crash was associated with a dramatic and permanent steepening of the implied volatility curve for equity index options, despite minimal changes in aggregate consumption. We explain these events within a general equilibrium framework in which expected endowment growth and economic...

Option market prices have often been regarded as a window on investor sentiment about the future price behavior of the underlying asset. Such prices can be very different from model prices and have long been noted by implied volatility plots revealing “smiles” or “smirks”. In this paper...

We use a series of different approaches to extract information about crash risk from option prices for the Euro-Dollar exchange rate, with each step sharpening the focus on extracting more specific measures of crash risk around dates of ECB measures of Unconventional Monetary Policy. Several...