FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

30 Pages Posted: 7 Mar 2023 Last revised: 11 Apr 2023

See all articles by Vedant Choudhary

Vedant Choudhary

University of Toronto - Department of Statistical Sciences

Sebastian Jaimungal

University of Toronto - Department of Statistics

Maxime Bergeron

Riskfuel Analytics

Date Written: March 3, 2023

Abstract

Here, we introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability integral transform penalty to reduce model misspecification. We demonstrate that learning the joint dynamics of IV surfaces and prices produces market scenarios that are consistent with historical features and lie within the sub-manifold of surfaces that are essentially free of static arbitrage. Finally, we demonstrate that delta hedging using the simulated surfaces generates profit and loss (P&L) distributions that are consistent with realised P&Ls.

Keywords: generative models, neural SDEs, functional data analysis, implied volatility

JEL Classification: G1, G12, C22, C45, C63

Suggested Citation

Choudhary, Vedant and Jaimungal, Sebastian and Bergeron, Maxime, FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs (March 3, 2023). Available at SSRN: https://ssrn.com/abstract=4377204 or http://dx.doi.org/10.2139/ssrn.4377204

Vedant Choudhary

University of Toronto - Department of Statistical Sciences ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Maxime Bergeron

Riskfuel Analytics ( email )

Toronto
Canada

HOME PAGE: http://https://riskfuel.com/

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