Pricing American options under rough volatility using deep-signatures and signature-kernels
Pricing American options under rough volatility using deep-signatures and signature-kernels
This paper extends signature-based methods for optimal stopping to price American options under rough volatility models, specifically rough Bergomi and rough Heston. The authors build on prior work that used linear functionals of the truncated signature, introducing deep-signature (combining signatures with deep neural networks) and signature-kernel (using kernel ridge regression) approaches. Both primal (Longstaff-Schwartz) and dual (martingale) formulations are implemented, providing lower and upper bounds for option prices.
Numerical experiments show that all three methods yield tight price bounds, with a gap of approximately 1% for the rough Bergomi model with Hurst index 0.07. For the primal problem, linear and kernel methods perform slightly better, while for the dual problem, the neural-network-based method shows clear advantages. The study also analyzes the importance of signature components, finding that all components matter in the primal case but only a few are relevant in the dual case, suggesting potential for dimension reduction. Overall, the paper demonstrates that signature-based methods are effective for non-Markovian optimal stopping problems in finance.
Highlights
- 1Extends signature-based primal and dual optimal stopping methods to non-Markovian rough volatility models.
- 2Integrates deep-signature and signature-kernel learning for pricing American options.
- 3Provides tight price bounds (≈1% gap) for rough Bergomi model with Hurst index H=0.07.
- 4Compares linear, deep neural network, and kernel methods for both primal and dual formulations.
- 5Demonstrates that neural-network-based dual methods outperform linear approaches.
Methods
- MSignature-based primal Longstaff-Schwartz algorithm using linear, deep neural network, and kernel approximations of continuation values.
- MSignature-based dual martingale method using linear, deep neural network, and kernel approximations of martingale integrands.
- MDeep-signature learning: combining truncated signatures with deep neural networks.
- MSignature-kernel learning: using kernel ridge regression with the signature kernel.
Results
- RFor rough Bergomi model (H=0.07), primal and dual bounds yield a tight gap of about 1%.
- RAll three methods (linear, DNN, kernel) perform well for primal problem; linear and kernel have mild advantages.
- RFor dual problem, neural-network-based method outperforms linear and kernel approaches.
- RTraining error decreases with number of training samples for all methods.
- RIn primal problem, all signature components matter; in dual problem, only few components are important.
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