Credit Risk Behind The Smile

We develop a framework for estimating corporate credit risk from equity implied-volatility (IV) surfaces when the target firm's CDS spread or credit rating is unavailable. Within a stochastic-variance structural model, we establish conditional identification of fixed-horizon default probabilities from the complete IV coefficient sequence, together with a finite-order stability bound. We use estimated IV coefficients in penalised mappings for log CDS spreads and rating probabilities. Simulations support a quadratic mapping based on four second-order coefficients as a parsimonious and accurate approximation, including when correlations vary across firms. Using daily data for 397 firms from 2018 to 2025, we find that the quadratic specification outperforms four structural benchmarks in held-out-firm predictions of CDS spreads and ratings. Its CDS predictions achieve higher \(R^2\) and lower RMSE than these benchmarks and are comparable to predictions based on observed ratings. These results support using equity options to recover credit information, with mappings learned from firms whose credit outcomes are observed.