ON DEEP LEARNING for OPTION PRICING in LOCAL VOLATILITY MODELS

We study neural network approximation of the solution to boundary value problem for Black-Scholes-Merton partial differential equation for a European call option price, when model volatility is a function of underlying asset price and time (local volatility model). Strike-price and expiry day of the option are assumed to be fixed. An approximation to option price in local volatility model is obtained via deep learning with deep Galerkin method (DGM), making use of the neural network of special architecture 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 volatility models are described in detail. Computational experiment with DGM neural network is performed to evaluate the quality of neural network approximation for hyperbolic sine local volatility model with known exact closed form option price. The quality of the neural network approximation is estimated with mean absolute error, mean squared error and coefficient of determination. The computational experiment demonstrates that DGM neural network approximation converges to a European call option price of the local volatility model with acceptable accuracy. © 2021 CEUR-WS. All rights reserved.