Deep Local Volatility

Marc Chataigner, Stéphane Crépey and Matthew Dixon
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Marc Chataigner: Department of Mathematics, University of Evry, Paris Saclay, 91100 Essonne, France
Stéphane Crépey: Department of Mathematics, University of Evry, Paris Saclay, 91100 Essonne, France
Matthew Dixon: Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616-3793, USA

Risks, 2020, vol. 8, issue 3, 1-18

Abstract: Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation of European vanilla option prices which jointly yields the full surface of local volatilities. We demonstrate the modification of the loss function or the feed forward network architecture to enforce (hard constraints approach) or favor (soft constraints approach) the no-arbitrage conditions and we specify the experimental design parameters that are needed for adequate performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option prices, during the network fitting. Our methodology is benchmarked numerically on real datasets of DAX vanilla options.

Keywords: option pricing; neural networks; no-arbitrage; local volatility (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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