# Risk-Neutral Market Simulation

arXiv: https://arxiv.org/abs/2202.13996 · HTML: https://mlsanity.com/paper/2202.13996/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 16 of 16)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Normalizing Flows on Riemannian Manifolds](https://mlsanity.com/paper/1611.02304/) (2016)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [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)
- [Robust pricing and hedging via neural SDEs](https://mlsanity.com/paper/2007.04154/) (2020)
- [Arbitrage-free neural-SDE market models](https://mlsanity.com/paper/2105.11053/) (2021)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures](https://mlsanity.com/paper/2111.07844/) (2021)
- [Estimating risks of option books using neural-SDE market models](https://mlsanity.com/paper/2202.07148/) (2022)

## Built on by (most cited first, 2 of 2)

- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Sig-Splines: universal approximation and convex calibration of time series generative models](https://mlsanity.com/paper/2307.09767/) (2023)

## Abstract (arXiv)

We develop a risk-neutral spot and equity option market simulator for a single underlying, under which the joint market process is a martingale. We leverage an efficient low-dimensional representation of the market which preserves no static arbitrage, and employ neural spline flows to simulate samples which are free from conditional drifts and are highly realistic in the sense that among all possible risk-neutral simulators, the obtained risk-neutral simulator is the closest to the historical data with respect to the Kullback-Leibler divergence. Numerical experiments demonstrate the effectiveness and highlight both drift removal and fidelity of the calibrated simulator.