Estimation of rare disaster concerns from option prices—An arbitrage‐free RND‐based smile construction approach

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 ${\mathbb{RIX}}$) when event risk is high.