26 Pages Posted: 10 May 2021
Date Written: May 5, 2021
In this paper we present a method for calculating the entire hedge surface of a derivative who’s future underlying asset has been simulated by a market simulator for example with the Monte Carlo method. Our method is built from work on penalized filtering techniques and is applied on a grid of hedges. Example using basis functions are also provided and we discuss the connection between penalization and use of basis functions. The method is tested on a a number of classical examples e.g. geometrical Brownian motion, the Heston model and the local volatility models with transaction costs. The results are very convincing in that for reasonable data sizes of just a couple of thousand data points, a working hedge function can be estimated. We believe that the generality of our method can be a competitive alternative to (or be combined with) recent methods that utilize deep learning for calculating hedges.
Keywords: pricing, derivative, hedging, filtering, deep hedging, simulation
JEL Classification: C61, C63, C67, G13
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