Dynamic hedging of option portfolios requires a state vector that captures information from both the underlying asset and the option market. Incorporating the full implied volatility surface raises two challenges: its cross-section must be summarized by a parsimonious set of state variables, and the resulting dynamic optimization problem becomes too high-dimensional for conventional Bellman recursions. We address these challenges using implied volatility factor models and reinforcement learning.

For S&P 500 index options, five economically interpretable factors summarize the implied volatility surface and enter a joint model for index returns and surface dynamics. This model provides the market simulator used to train a recurrent deep-hedging strategy with the index and an option as hedging instruments, while explicitly accounting for transaction costs. Simulation experiments and a historical out-of-sample backtest compare the resulting strategies with conventional delta and delta-gamma hedging and assess the contribution of implied volatility information to risk reduction.

The final part of the presentation considers individual-stock options. A deep implied volatility factor model incorporates time to earnings announcements while retaining a parsimonious daily representation of the surface, with applications to risk-neutral density estimation and stock-specific volatility indices.

Joint work with Pascal François, Frédéric Godin, Sébastien Legros, and Carlos O. Pérez-Mendoza.

Bio: Geneviève Gauthier holds a PhD in Mathematics and is Professor in the Department of Decision Sciences at HEC Montréal, where she holds a Research Professorship in Financial Engineering. In 2018, she received the Statistical Society of Canada Award for Impact of Applied and Collaborative Work for her outstanding contributions to the promotion of innovative statistical methodologies in financial engineering.

Her research focuses on financial engineering, mathematical finance, and financial econometrics, with applications to derivative pricing, risk management, volatility modelling, credit risk, and financial and energy markets. Her work combines stochastic modelling, filtering methods, simulation, high-frequency data, and machine learning.