Arbitrage-free neural-SDE market models

TL;DR

This paper introduces a neural network-based, arbitrage-free nonparametric model for joint dynamics of liquid vanilla options, enabling realistic pricing and risk management of illiquid derivatives.

Contribution

It develops a neural SDE framework that enforces no-arbitrage constraints and can be calibrated from market data, advancing the modeling of option prices.

Findings

Model respects no-arbitrage conditions

Neural SDEs calibrated to simulated data

Validated with Heston model data

Abstract

Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting underlying financial constraints and while being practically implementable. We derive a state space for prices which are free from static (or model-independent) arbitrage and study the inference problem where a model is learnt from discrete time series data of stock and option prices. We use neural networks as function approximators for the drift and diffusion of the modelled SDE system, and impose constraints on the neural nets such that no-arbitrage conditions are preserved. In particular, we give methods to calibrate \textit{neural SDE} models which are guaranteed to satisfy a set of linear inequalities. We validate our approach with numerical experiments using data generated from a Heston stochastic local volatility model.