Implied Risk Aversion Smile

How does the market makers' aversion to unhedgeable risks influence option prices? We answer this question by introducing a new structural approach: deep replication. With this method, we extract the risk aversion of S&P500 options per contract and per day. Cross-sectionally, we show the existence of a risk aversion smile reminiscent of the Black-Scholes volatility smile. Across time, we measure a change following 2008, with put options exhibiting a higher average risk aversion premium in the post-crisis environment. With a stylized model and empirical analysis, we demonstrate a link between the risk aversion smile, excess inventory, and unhedgeable risks