Résumé
The undeniable centrality of volatility surfaces (VSs) in modern quantitative finance has inspired many hand-crafted arbitrage-free VS models; each designed to capture specific stylized features of empirically observed VSs; nevertheless, there remains no generic VS framework devoid of static arbitrage. Though deep learning pipelines provide hope for generic VS modelling, these AI-based approaches presently fail as they typically violate static no-arbitrage conditions. We close this gap in the literature. Our analysis begins with the newly uncovered observation that empirical VS data exhibits log-complete monotonicity in their strike price. We then construct a universal two-layer deep learning model representative of this class of arbitrage-free VSs. The structured weights and biases constraint and the very-specific choices of activation functions allow us to guarantee that our models are always free of static arbitrage and the observed log-complete monotonicity in the strike observed in real-world VS data, while maintaining universality. Additionally, our deep learner’s structure grants us access to a Fourier-analytic training procedure, which is much more efficient than out-of-the-box (stochastic) gradient-descent-based optimization. Our method is implemented on real-world volatility data, where we achieve state-of-the-art reconstruction performance.
Joint work: Yannick Limmer and Blanka Horvath (Oxford)
Biographie
Anastasis is an assistant professor at McMaster University working on the analytic and statistical foundations of AI and theoretically-guided deep learning in finance. His work aims at understanding the behaviour and properties of these models from the ground up, and using his findings to develop new principled AI which can leverage structures in finance, stochastic processes, games, and PDEs problems to obtain guaranteed scalable and predictive computational pipelines.
Anastasis did his PhD at Concordia university in mathematical finance and his Masters at l’Université de Montréal in mathematics, before moving to ETH Zürich for his postdoc in deep learning for finance and then to the University of Basel to work on geometric deep learning. Since starting his faculty position, Anastasis has supervised 10 students including postdoc and PhD students to honors undergraduate students.