Variational Autoencoders: A Hands-Off Approach to Volatility

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 are incomplete, and it is necessary to estimate missing points on partially observed surfaces. In this article, the authors show how variational autoencoders can be used to model volatility surfaces. The first step is to train the model, deriving 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 the latent variables that fits available data as closely as possible. The trained variational autoencoder can also be used to generate synthetic-yet-realistic surfaces, which can be used in stress testing, in market simulators for developing quantitative investment strategies, and for the valuation of exotic options. The authors illustrate their procedure using foreign exchange market data.