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Variational Autoencoders: A Hands-Off Approach to Volatility

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  • Maxime Bergeron
  • Nicholas Fung
  • John Hull
  • Zissis Poulos

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.

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  • Maxime Bergeron & Nicholas Fung & John Hull & Zissis Poulos, 2021. "Variational Autoencoders: A Hands-Off Approach to Volatility," Papers 2102.03945, arXiv.org.
    • Handle: RePEc:arx:papers:2102.03945
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
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    Cited by:

    1. Magnus Wiese & Ben Wood & Alexandre Pachoud & Ralf Korn & Hans Buehler & Phillip Murray & Lianjun Bai, 2021. "Multi-Asset Spot and Option Market Simulation," Papers 2112.06823, arXiv.org.
    2. Wenyong Zhang & Lingfei Li & Gongqiu Zhang, 2021. "A Two-Step Framework for Arbitrage-Free Prediction of the Implied Volatility Surface," Papers 2106.07177, arXiv.org, revised Jan 2022.
    3. Arian, Hamid & Moghimi, Mehrdad & Tabatabaei, Ehsan & Zamani, Shiva, 2022. "Encoded Value-at-Risk: A machine learning approach for portfolio risk measurement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 500-525.
    4. Brian Ning & Sebastian Jaimungal & Xiaorong Zhang & Maxime Bergeron, 2021. "Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders," Papers 2108.04941, arXiv.org, revised Jan 2022.
    5. Hans Buehler & Phillip Murray & Mikko S. Pakkanen & Ben Wood, 2021. "Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics," Papers 2103.11948, arXiv.org, revised Jul 2021.
    6. S'andor Kuns'agi-M'at'e & G'abor F'ath & Istv'an Csabai & G'abor Moln'ar-S'aska, 2022. "Deep Weighted Monte Carlo: A hybrid option pricing framework using neural networks," Papers 2208.14038, arXiv.org, revised Dec 2022.

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