Next Article in Journal
Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits
Next Article in Special Issue
Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II
Previous Article in Journal
Can Sustainable Investment Yield Better Financial Returns: A Comparative Study of ESG Indices and MSCI Indices
Open AccessArticle

Pricing Options and Computing Implied Volatilities using Neural Networks

1
Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Building 28, Mourik Broekmanweg 6, 2628 XE Delft, The Netherlands
2
Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands
*
Author to whom correspondence should be addressed.
Risks 2019, 7(1), 16; https://doi.org/10.3390/risks7010016
Received: 8 January 2019 / Revised: 3 February 2019 / Accepted: 6 February 2019 / Published: 9 February 2019
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. View Full-Text
Keywords: machine learning; neural networks; computational finance; option pricing; implied volatility; GPU; Black-Scholes; Heston machine learning; neural networks; computational finance; option pricing; implied volatility; GPU; Black-Scholes; Heston
Show Figures

Figure 1

MDPI and ACS Style

Liu, S.; Oosterlee, C.W.; Bohte, S.M. Pricing Options and Computing Implied Volatilities using Neural Networks. Risks 2019, 7, 16.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop