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Paper · 2007.04154 · 2020

Robust pricing and hedging via neural SDEs

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 24 functions out of this paper's own repositories and ran 16 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
msabvid/robust_nsde canonical 0 of 2
ericavanee/bicausal_wasserstein_mtglproj pwc_unofficial 16 of 22
FunctionStatusWhere it lives
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code served (permissive licence) · get_code("5857af5cae346057")
cutoff Ran ericavanee/bicausal_wasserstein_mtglproj/src/adapted_mtgl/mtgl_test/mtgl.py
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generate_grid_points Ran ericavanee/bicausal_wasserstein_mtglproj/src/adapted_mtgl/mtgl_test/multiD.py
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get_bounds Ran ericavanee/bicausal_wasserstein_mtglproj/src/adapted_mtgl/mtgl_test/mtgl.py
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get_params Ran ericavanee/bicausal_wasserstein_mtglproj/src/adapted_mtgl/utils.py
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inverse Ran ericavanee/bicausal_wasserstein_mtglproj/applications/markov/bdd_fun.py
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kernel Ran ericavanee/bicausal_wasserstein_mtglproj/src/adapted_mtgl/mtgl_test/mtgl.py
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map_to_grid Ran ericavanee/bicausal_wasserstein_mtglproj/src/adapted_mtgl/mtgl_test/ada_emp_dist.py
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tanh Ran ericavanee/bicausal_wasserstein_mtglproj/applications/markov/bdd_fun.py
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train_nsde Not yet run msabvid/robust_nsde/nsde_LV.py
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Abstract

Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Any given model provides only a crude approximation to reality and the risk of using an inadequate model is hard to detect and quantify. By contrast, modern data science techniques are opening the door to more robust and data-driven model selection mechanisms. However, most machine learning models are "black-boxes" as individual parameters do not have meaningful interpretation. The aim of this paper is to combine the above approaches achieving the best of both worlds. Combining neural networks with risk models based on classical stochastic differential equations (SDEs), we find robust bounds for prices of derivatives and the corresponding hedging strategies while incorporating relevant market data. The resulting model called neural SDE is an instantiation of generative models and is closely linked with the theory of causal optimal transport. Neural SDEs allow consistent calibration under both the risk-neutral and the real-world measures. Thus the model can be used to simulate market scenarios needed for assessing risk profiles and hedging strategies. We develop and analyse novel algorithms needed for efficient use of neural SDEs. We validate our approach with numerical experiments using both local and stochastic volatility models.

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