This research addresses the estimation of measures of rare disaster concerns from option prices. We propose a new smile construction approach to obtain the required continuum of implied volatilities from discretely sampled observations that are affected by microstructure noise. We extrapolate implied volatilities of far out-of-the-money options by modeling the tails of the risk-neutral return distribution (RND) ensuring that option prices do not admit arbitrage. Our numerical analysis and empirical application show that the RND-based approach consistently outperforms standard techniques. It substantially reduces estimation errors resulting in considerably higher estimates of the rare disaster concern index (RIX) when event risk is high.