Extensive networks would eliminate the demand for pricing formulas

TL;DR

This paper demonstrates that extensive neural networks trained on GPU-generated implied volatilities can replace traditional pricing formulas for the SABR model, achieving high accuracy and efficiency without explicit formulas.

Contribution

The study introduces a neural network approach that eliminates the need for explicit pricing formulas in the SABR model, with a novel error analysis method applicable to other models.

Findings

Neural networks match Monte Carlo accuracy for SABR implied volatilities.

The approach reduces simulation noise and improves efficiency.

The method is extendable to other models lacking explicit formulas.

Abstract

In this study, we generate a large number of implied volatilities for the Stochastic Alpha Beta Rho (SABR) model using a graphics processing unit (GPU) based simulation and enable an extensive neural network to learn them. This model does not have any exact pricing formulas for vanilla options, and neural networks have an outstanding ability to approximate various functions. Surprisingly, the network reduces the simulation noises by itself, thereby achieving as much accuracy as the Monte-Carlo simulation. Extremely high accuracy cannot be attained via existing approximate formulas. Moreover, the network is as efficient as the approaches based on the formulas. When evaluating based on high accuracy and efficiency, extensive networks can eliminate the necessity of the pricing formulas for the SABR model. Another significant contribution is that a novel method is proposed to examine the errors based on nonlinear regression. This approach is easily extendable to other pricing models for which it is hard to induce analytic formulas.