Mathematical and Computational Finance Seminar

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.

Markets change regime. A trend fades, order flow turns, and a signal that made money last week starts to lose it. Traders often monitor these breaks with a sequential alarm, which fires once the evidence against the current regime is strong enough. But alarms can be late or simply wrong, so how much should a trader trust one? Our main result is a general theorem that characterises the optimal strategy for a broad class of trading problems in which decisions rely on such an alarm. We apply it to two central problems in finance, namely executing a large order with price impact and allocating a portfolio between risky assets and cash. In both cases, the theorem gives explicit strategies. In execution, the trader does not wait for the alarm, and positions shift ahead of it based on how likely it is to fire before the horizon ends. We also show that the alarm should be calibrated to the trading objective rather than to a purely statistical false-alarm rate, because false alarms and late alarms have different costs in each setting. Finally, simulations compare these strategies with simple rules a trading desk might use, showing where the extra complexity pays off and where it does not.