Variational Autoencoders: A Hands-Off Approach to Volatility

28 Pages Posted: 19 Apr 2021

See all articles by Maxime Bergeron

Maxime Bergeron

Riskfuel Analytics

Nicholas Fung

University of Toronto - The Edward S. Rogers Sr. Department of Electrical and Computer Engineering

Zissis Poulos

University of Toronto - Rotman School of Management

John C. Hull

University of Toronto - Rotman School of Management

Andreas Veneris

University of Toronto

Date Written: April 15, 2021

Abstract

A volatility surface is an important tool for pricing and hedging derivatives. The surface shows the volatility that is implied by the market price of an option on an asset as a function of the option's strike price and maturity. Often, market data is incomplete and it is necessary to estimate missing points on partially observed surfaces. In this paper, we show how variational autoencoders can be used for this task. The first step is to derive latent variables that can be used to construct synthetic volatility surfaces that are indistinguishable from those observed historically. The second step is to determine the synthetic surface generated by our latent variables that fits available data as closely as possible. As a dividend of our first step, the synthetic surfaces produced can also be used in stress testing, in market simulators for developing quantitative investment strategies, and for the valuation of exotic options. We illustrate our procedure and demonstrate its power using foreign exchange market data.

Keywords: Derivatives; Unsupervised learning; Variational autoencoders

JEL Classification: G10, G20

Suggested Citation

Bergeron, Maxime and Fung, Nicholas and Poulos, Zissis and Hull, John C. and Veneris, Andreas, Variational Autoencoders: A Hands-Off Approach to Volatility (April 15, 2021). Available at SSRN: https://ssrn.com/abstract=3827447 or http://dx.doi.org/10.2139/ssrn.3827447

Maxime Bergeron

Riskfuel Analytics ( email )

Toronto
Canada

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

Nicholas Fung (Contact Author)

University of Toronto - The Edward S. Rogers Sr. Department of Electrical and Computer Engineering ( email )

Toronto
Canada

Zissis Poulos

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

John C. Hull

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada
(416) 978-8615 (Phone)
416-971-3048 (Fax)

Andreas Veneris

University of Toronto ( email )

Toronto, Ontario M5S 3G8
Canada

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