Deep Local Volatility

Clicks: 111
ID: 111899
2020
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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.
Reference Key
chataigner2020risksdeep Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Marc Chataigner;Stéphane Crépey;Matthew Dixon;Chataigner, Marc;Crépey, Stéphane;Dixon, Matthew;
Journal risks
Year 2020
DOI
10.3390/risks8030082
URL
https://www.mdpi.com/2227-9091/8/3/82/htm
Keywords
neural networks option pricing no-arbitrage local volatility

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