# Samuel Cohen: Arbitrage-free Neural-SDE Market models

**Time: **
Mon 2021-11-29 15.15 - 16.15

**Location: **
Zoom, Meeting ID: 636 3541 3752

**Lecturer: **
Samuel Cohen (Oxford University)

### Abstract

Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. In this talk we will develop a nonparametric model for the European options book respecting underlying financial constraints and while being practically implementable. In particular, we will consider 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 *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 volatility model, and with observed market data.