Open AccessON DEEP LEARNING FOR OPTION PRICING IN LOCAL VOLATILITY MODELS
Author(s) -
S. G. Shorokhov
Publication year - 2021
Publication title -
9th international conference "distributed computing and grid technologies in science and education"
Language(s) - English
Resource type - Conference proceedings
DOI - 10.54546/mlit.2021.17.84.001
Subject(s) - implied volatility , stochastic volatility , volatility (finance) , artificial neural network , local volatility , volatility smile , valuation of options , econometrics , black–scholes model , mathematical optimization , computer science , mathematics , artificial intelligence
We study neural network approximation of the solution to boundary value problem for Black-ScholesMerton partial differential equation for a European call option price, when model volatility is afunction of underlying asset price and time (local volatility model). Strike-price and expiry day of theoption are assumed to be fixed. An approximation to option price in local volatility model is obtainedvia deep learning with deep Galerkin method (DGM), making use of the neural network of specialarchitecture and stochastic gradient descent on a sequence of random time and underlying price points.Architecture of the neural network and the algorithm of its training for option pricing in local volatilitymodels are described in detail. Computational experiment with DGM neural network is performed toevaluate the quality of neural network approximation for hyperbolic sine local volatility model withknown exact closed form option price. The quality of the neural network approximation is estimatedwith mean absolute error, mean squared error and coefficient of determination. The computationalexperiment demonstrates that DGM neural network approximation converges to a European calloption price of the local volatility model with acceptable accuracy.