Pricing Options and Computing Implied Volatilities using Neural Networks

Shuaiqiang Liu,Sander Bohte,Cornelis Oosterlee

doi:10.3390/risks7010016

Shuaiqiang Liu, Sander Bohte + Show 1 more

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https://doi.org/10.3390/risks7010016

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Abstract

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

Highlights

In computational finance, numerical methods are commonly used for the valuation of financial derivatives and in modern risk management
We show the performance of the Artificial Neural Network (ANN) for solving the financial models, based on the following accuracy metrics, mean squared error (MSE) =
In this paper we have proposed an ANN approach to reduce the computing time of pricing financial options, especially for high-dimensional financial models

Summary

Introduction

Numerical methods are commonly used for the valuation of financial derivatives and in modern risk management. Speaking, advanced financial asset models are able to capture nonlinear features that are observed in the financial markets. These asset price models are often multi-dimensional, and, as a consequence, do not give rise to closed-form solutions for option values. The open parameters in the asset price model need to be fitted. This is typically not done by historical asset prices, but by means of option prices, i.e., by matching the market prices of heavily traded options to the option prices from the mathematical model, under the so-called risk-neutral probability measure. Efficient numerical computation is increasingly important in financial risk management, especially when we deal with real-time risk management (e.g., high frequency trading) or counterparty credit risk issues, where a trade-off between efficiency and accuracy seems often inevitable

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