Arbitrage-Free Neural-SDE Market Models

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