Deep local volatility

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...

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Bibliographic Details
Published in:Risks (Basel) 2020-09, Vol.8 (3), p.1-18
Main Authors: Chataigner, Marc, Crépey, Stéphane, Dixon, Matthew F
Format: Article
Language:English
Subjects:
Approximation
Arbitrage
Computational Finance
Hedging
local volatility
Machine learning
Market prices
Neural networks
no-arbitrage
option pricing
Put & call options
Quantitative Finance
Securities prices
Volatility
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Summary: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.
ISSN:2227-9091
2227-9091
DOI:10.3390/risks8030082