Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders

• URL: http://arxiv.org/abs/2108.04941v1
• Date: Tue, 10 Aug 2021 21:56:19 GMT
• Title: Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders
• Authors: Brian Ning, Sebastian Jaimungal, Xiaorong Zhang, Maxime Bergeron
• Abstract summary: We propose a hybrid method for generating arbitrage-free implied volatility surfaces consistent with historical data. We focus on two classes of SDE models: regime switching models and L'evy additive processes.
• Score: 0.3441021278275805
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free Variational Autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and L\'evy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior distribution on the latent space, decoding to obtain SDE model parameters, and finally mapping those parameters to IV surfaces.

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