The smirk in the S&P500 futures options prices: a linearized factor analysis

In the S&P500 futures options, we identify three factors, corresponding to movements in the underlying, parallel movements, and tilting of the cross section of implied volatilities (the “smirk factor”). We relate these factors non-linearly to movements in the option prices. They seem to be diffusive in nature, have significant associated risk premia, and can account for an overwhelming part of the option price movements. We interpret the options smirk, which is the notion that out-of-the-money (OTM) puts seem expensive relative to OTM calls, in terms of the prices of these risk factors. Going short OTM puts and long OTM calls, corresponding to the third factor, makes a profit on average, but this corresponds to its risk premium, and does not represent a market inefficiency. Our smirk factor is useful for hedging option portfolios, but seems unrelated to movements in the underlying, and does not fit into the framework of the jump-diffusion models.