# Multi-Asset Spot and Option Market Simulation

arXiv: https://arxiv.org/abs/2112.06823 · HTML: https://mlsanity.com/paper/2112.06823/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows](https://mlsanity.com/paper/2002.10516/) (2020)
- [Cubic-Spline Flows](https://mlsanity.com/paper/1906.02145/) (2019)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [A generative adversarial network approach to calibration of local stochastic volatility models](https://mlsanity.com/paper/2005.02505/) (2020)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Noise Regularization for Conditional Density Estimation](https://mlsanity.com/paper/1907.08982/) (2019)
- [Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combination](https://mlsanity.com/paper/1901.01751/) (2019)
- [Arbitrage-free neural-SDE market models](https://mlsanity.com/paper/2105.11053/) (2021)
- [CorrGAN: Sampling Realistic Financial Correlation Matrices Using Generative Adversarial Networks](https://mlsanity.com/paper/1910.09504/) (2019)
- [Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures](https://mlsanity.com/paper/2111.07844/) (2021)
- [Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders](https://mlsanity.com/paper/2108.04941/) (2021)
- [Monte Carlo Simulation of SDEs using GANs](https://mlsanity.com/paper/2104.01437/) (2021)

## Built on by (most cited first, 17 of 17)

- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [Deep Hedging: Continuous Reinforcement Learning for Hedging of General Portfolios across Multiple Risk Aversions](https://mlsanity.com/paper/2207.07467/) (2022)
- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [Simulating financial time series using attention](https://mlsanity.com/paper/2207.00493/) (2022)
- [Generative Machine Learning for Multivariate Equity Returns](https://mlsanity.com/paper/2311.14735/) (2023)
- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [Estimating risks of option books using neural-SDE market models](https://mlsanity.com/paper/2202.07148/) (2022)
- [Risk-Neutral Market Simulation](https://mlsanity.com/paper/2202.13996/) (2022)
- [Flexible Tails for Normalising Flows, with Application to the Modelling of Financial Return Data](https://mlsanity.com/paper/2311.00580/) (2023)
- [NeuralFactors: A Novel Factor Learning Approach to Generative Modeling of Equities](https://mlsanity.com/paper/2408.01499/) (2024)
- [Implementing Quantum Generative Adversarial Network (qGAN) and QCBM in Finance](https://mlsanity.com/paper/2308.08448/) (2023)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)
- [DYSANOS Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces](https://mlsanity.com/paper/2608.12587/) (2026)
- [Sig-Splines: universal approximation and convex calibration of time series generative models](https://mlsanity.com/paper/2307.09767/) (2023)
- [Robust Control under Stationary Ambiguity](https://mlsanity.com/paper/2608.04832/) (2026)

## Abstract (arXiv)

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.