Deep Replication

Abstract

How does the market makers' aversion to unhedgeable risks influence option prices? We answer this question by introducing a structural approach: deep replication. With it, we extract the risk aversion of a representative market maker for S&P500 options per contract and per day. Cross-sectionally, we show the existence of a risk aversion smile across the options' moneyness. Across time, we measure a regime 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, inventory, and unhedgeable risks.

Keywords: Deep Learning, Agent Preferences, Risk Aversion, Volatility Smile, Asset Pricing

JEL Classification: C61, C73, D82, D86, E61