Arbitrage-free neural-SDE market models
This addresses the need for accurate and constraint-respecting models in finance for pricing illiquid derivatives and managing option trade risks, representing an incremental improvement by applying neural networks to enforce no-arbitrage conditions in SDE systems.
The paper tackled the problem of modeling joint dynamics of liquid vanilla options for arbitrage-free pricing and risk management by developing a nonparametric neural-SDE model that respects financial constraints and is practically implementable, validated through numerical experiments with data from a Heston stochastic local volatility model.
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.