Wilmott Magazine: July 2023 issue – 50th Anniversary of Black-Scholes-Merton Part 2

Author: Jörg Kienitz

Delta Hedging in the Age of Machine Learning

 Abstract: 

A data driven and model free approach termed GMM-Proxy-Hedge for hedging is introduced. The method uses realizations of stochastic quantities on a discrete time-grid and combines fitted Gaussian Mixture Distributions (GMM), being an established method from statistical learning, see, with classic analytic techniques based on the properties of the Gaussian distribution. It leads to an analytic expression for a hedge with respect to a chosen proxy.Taking for instance the underlying as the proxy, it gives the time-discrete minimal variance delta hedge. For the classical setting of the

Black-Scholes-Merton model this hedge corresponds to discretely applied standard delta hedge. We give a detailed outline of the method and apply it for hedging vanilla,early exercise and high-dimensional exotic options. For illustration we generate data using challenging models including the rough Bergomi,

or the Bates model in one and multiple dimensions as well as generative methods based on (Variational) Autoencoders or Generative Adversarial Networks.

Read full paper here

J. Kienitz, “Hedging in the Age of Statistical Learning,” Wilmott, vol. 2023, iss. 126, p. 94–102, 2023.

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