Deep calibration of rough stochastic volatility models
Deep calibration of rough stochastic volatility models
The paper introduces a deep calibration method for rough stochastic volatility models, which are known for their ability to capture key market features like the exploding at-the-money volatility skew but are computationally expensive due to non-Markovian dynamics. The authors propose replacing costly Monte Carlo simulations with a pre-trained neural network that approximates the implied volatility map. This network is trained on synthetically generated data and then integrated into a Levenberg-Marquardt optimization routine, providing fast evaluations and automatic differentiation for Jacobian computation. The method is applied to the Heston model and the rough Bergomi model, demonstrating high accuracy and significant speed improvements. Additionally, Bayesian inference is used to quantify parameter uncertainty, confirming that the neural network-based calibration recovers true or previously reported parameter values. The approach enables efficient calibration of complex models, making them practical for real-world applications.
Highlights
- 1Proposes deep calibration combining Levenberg-Marquardt with neural network regression to replace expensive Monte Carlo simulations.
- 2Demonstrates the approach on Heston and rough Bergomi models, achieving high accuracy and speed.
- 3Uses Bayesian inference to quantify uncertainty in calibrated parameters, recovering true or previously reported values.
- 4Neural network provides fast Jacobian approximations via automatic differentiation, enabling efficient calibration.
Methods
- MLevenberg-Marquardt algorithm for nonlinear least squares optimization.
- MFully-connected neural network (FCNN) with ReLU activation for regression of the implied volatility map.
- MSynthetic data generation using Monte Carlo simulations for training the neural network.
- MBayesian nonlinear regression for posterior inference of model parameters.
Results
- RNeural network approximates implied volatility with small relative errors across liquid parts of the surface.
- RCalibration with neural network is competitive with Heston pricing methods and significantly faster than rough Bergomi Monte Carlo.
- RPosterior distributions from Bayesian regression correctly identify sensible parameter regions and peaks near true or reported values.
- RThe approach recovers characteristic implied volatility smiles and at-the-money skews.
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