Sig-SDEs model for quantitative finance

TL;DR

The paper introduces Sig-SDE, a novel data-driven model for quantitative finance that integrates signature-based path transformations with neural SDEs, enabling better calibration and simulation of market scenarios.

Contribution

It presents the Sig-SDE framework, combining stochastic analysis and machine learning for improved model calibration and trajectory-based pricing in finance.

Findings

Successfully calibrates to exotic financial products.

Enables consistent calibration under different measures.

Demonstrates realistic market scenario simulations.

Abstract

Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance. In this work, we propose a novel framework for data-driven model selection by integrating a classical quantitative setup with a generative modelling approach. Leveraging the properties of the signature, a well-known path-transform from stochastic analysis that recently emerged as leading machine learning technology for learning time-series data, we develop the Sig-SDE model. Sig-SDE provides a new perspective on neural SDEs and can be calibrated to exotic financial products that depend, in a non-linear way, on the whole trajectory of asset prices. Furthermore, we our approach enables to consistently calibrate under the pricing measure $\mathbb Q$ and real-world measure $\mathbb P$. Finally, we demonstrate the ability of Sig-SDE to simulate future possible market scenarios needed for computing risk profiles or hedging strategies. Importantly, this new model is underpinned by rigorous mathematical analysis, that under appropriate conditions provides theoretical guarantees for convergence of the presented algorithms.