Machine Learning in Finance

Speaker: Milena Vuletić (University of Oxford)

Date/Time: Tuesday, 4/2, 7pm CET (10am PST, 1pm EST)

Title: VolGAN: a generative model for arbitrage-free implied volatility surfaces

Abstract: We introduce VolGAN, a generative model for arbitrage-free implied volatility surfaces. The model is trained on time series of implied volatility surfaces and underlying prices and is capable of generating realistic scenarios for joint dynamics of the implied volatility surface and the underlying asset. We illustrate the performance of the model by training it on SPX implied volatility time series and show that it is able to learn the covariance structure of the co-movements in implied volatilities and generate realistic dynamics for the (VIX) volatility index. In particular, the generative model is capable of simulating scenarios with non-Gaussian distributions of increments for state variables as well as time-varying correlations.

Speaker: Paul Hager (UT Berlin)

Date/Time: Tuesday, 4/2, 7pm CET (10am PST, 1pm EST)

Title: Advancing optimal stochastic control with signatures

Abstract: The role of signatures in solving non-Markovian control problems has been increasingly recognized, particularly in areas of mathematical finance, such as optimal execution, portfolio optimization, and the valuation of American options. In this work, we study a general class of differential equations driven by stochastic rough paths, where the control impacts the system's drift. In the theoretical aspect, we demonstrate that optimal controls can be approximated using linear and deep signature functionals. This includes a stability result for controlled rough differential equations and a refined lifting result for progressively measurable processes into continuous path-functionals. Building on these theoretical insights, we have developed a practical numerical methodology based on Monte-Carlo sampling and deep learning techniques. We demonstrate the efficiency of this methodology through numerical examples, including the optimal tracking of fractional Brownian motion, for which we provide exact theoretical benchmarks.