# A generative adversarial network approach to calibration of local stochastic volatility models

arXiv: https://arxiv.org/abs/2005.02505 · HTML: https://mlsanity.com/paper/2005.02505/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2020.

## Built on by (most cited first, 29 of 29)

- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality](https://mlsanity.com/paper/2106.08900/) (2021)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Reinforcement Learning with Dynamic Convex Risk Measures](https://mlsanity.com/paper/2112.13414/) (2021)
- [Arbitrage-free neural-SDE market models](https://mlsanity.com/paper/2105.11053/) (2021)
- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [Instance-Dependent Generalization Bounds via Optimal Transport](https://mlsanity.com/paper/2211.01258/) (2022)
- [Chaotic Hedging with Iterated Integrals and Neural Networks](https://mlsanity.com/paper/2209.10166/) (2022)
- [Deep neural network expressivity for optimal stopping problems](https://mlsanity.com/paper/2210.10443/) (2022)
- [FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs](https://mlsanity.com/paper/2303.00859/) (2023)
- [Monte Carlo Simulation of SDEs using GANs](https://mlsanity.com/paper/2104.01437/) (2021)
- [How (Implicit) Regularization of ReLU Neural Networks Characterizes the Learned Function -- Part II: the Multi-D Case of Two Layers with Random First Layer](https://mlsanity.com/paper/2303.11454/) (2023)
- [Machine learning for option pricing: an empirical investigation of network architectures](https://mlsanity.com/paper/2307.07657/) (2023)
- [Generative Adversarial Network: Some Analytical Perspectives](https://mlsanity.com/paper/2104.12210/) (2021)
- [Risk-Neutral Market Simulation](https://mlsanity.com/paper/2202.13996/) (2022)
- [Universal approximation property of neural stochastic differential equations](https://mlsanity.com/paper/2503.16696/) (2025)
- [Neural stochastic Volterra equations: learning path-dependent dynamics](https://mlsanity.com/paper/2407.19557/) (2024)
- [Efficient Neural SDE Training using Wiener-Space Cubature](https://mlsanity.com/paper/2502.12395/) (2025)
- [HGAN-SDEs: Learning Neural Stochastic Differential Equations with Hermite-Guided Adversarial Training](https://mlsanity.com/paper/2512.20272/) (2025)
- [Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective](https://mlsanity.com/paper/2203.06865/) (2022)
- [Directed Chain Generative Adversarial Networks](https://mlsanity.com/paper/2304.13131/) (2023)
- [High-Quality Synthetic Financial Time-Series using a GAN-Diffusion Framework](https://mlsanity.com/paper/2605.27113/) (2026)
- [Beyond the Smile: A Hybrid Convolutional VAE for Crypto Volatility Surfaces](https://mlsanity.com/paper/2606.16961/) (2026)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)
- [Amortizing the Calibration Triple: A Projection-Consistent Neural Operator for Local-Stochastic Volatility](https://mlsanity.com/paper/2608.01217/) (2026)
- [Asymptotically-informed neural networks for Black-Scholes implied volatility computation](https://mlsanity.com/paper/2609.05491/) (2026)
- [Shapley-based Structural Analysis of Neural Calibration for Stochastic Volatility Models](https://mlsanity.com/paper/2610.03076/) (2026)

## Abstract (arXiv)

We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family of feed-forward neural networks and learn their parameters directly from the available market option prices. This should be seen in the context of neural SDEs and (causal) generative adversarial networks: we generate volatility surfaces by specific neural SDEs, whose quality is assessed by quantifying, possibly in an adversarial manner, distances to market prices. The minimization of the calibration functional relies strongly on a variance reduction technique based on hedging and deep hedging, which is interesting in its own right: it allows the calculation of model prices and model implied volatilities in an accurate way using only small sets of sample paths. For numerical illustration we implement a SABR-type LSV model and conduct a thorough statistical performance analysis on many samples of implied volatility smiles, showing the accuracy and stability of the method.