Recovering Risk-Neutral Moments from Options

Extracting risk-neutral dependence from option prices has remained an open problem since Ross (1976). We propose a projection estimator that uses portfolios of observed options to approximate payoffs depending on multiple assets. The method delivers estimates of risk-neutral dependence in incomplete markets, improves univariate estimates, and yields a finite-sample error bound. Applying the method to two unexpected Swiss National Bank announcements about the EUR/CHF floor, we find that dependence accounts for two-thirds of the change in the probability that EUR/CHF and USD/CHF both fall sharply. A policy targeting EUR/CHF thus reshaped dependence in the CHF market.