Nonparametric estimation of equity return distribution from index options

I estimate a return distribution of an equity index from equity index option prices. I evaluate nonparametrically the option price function and a state price density at each 1-year return. Based on a model for dynamics of consumption growth and dividend growth, a real-world probability density of the index return is measured, resulting in both a high expected return of the index and a low riskless rate. The nonparametric SPD and the real-world density show fatter negative tails than the lognormal models of the Black-Sholes models have, implying the existence of disasters in the return process.