Recovering State Prices from Options

Extracting the joint risk-neutral distribution from option prices has remained an open problem since Ross (1976). We propose a projection-based estimator that approximates target payoffs over the entire state space using portfolios of observed options. The method estimates correlations and joint crash probabilities even when markets are incomplete, improves univariate estimates relative to Carr and Madan (2001(, and yields an explicit finite-sample bound interpretable as a measure of market incompleteness. Applying the method to two unexpected Swiss National Bank announcements about the EUR/CHF floor, we find that dependence, rather than marginal volatility, accounts for about two-thirds of the change in joint crash risk. A policy targeting one exchange rate reshaped the broader CHF currency market.