Multi-Asset Spot and Option Market Simulation

Abstract

We construct realistic spot and equity option market simulators for a single underlying on the basis of normalizing flows. We address the high-dimensionality of market observed call prices through an arbitrage-free autoencoder that approximates efficient low-dimensional representations of the prices while maintaining no static arbitrage in the reconstructed surface. Given a multi-asset universe, we leverage the conditional invertibility property of normalizing flows and introduce a scalable method to calibrate the joint distribution of a set of independent simulators while preserving the dynamics of each simulator. Empirical results highlight the goodness of the calibrated simulators and their fidelity.

Keywords: volatility surface, generative modeling, mathematical finance, time series, neural networks, options, normalizing flows, multi-asset markets, generative adversarial networks, autoencoder, copulas, risk management, hedging

JEL Classification: C15, C45, C5, C53, C6, C63, G00