Abstract.

We introduce a new deep learning–based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE, depending on forward curves rather than the whole path of the process, we develop a numerical scheme based on deep learning techniques. Numerical simulations suggest that the latter is a promising alternative to classical Monte Carlo simulations.

Keywords

  1. rough volatility
  2. deep learning
  3. path-dependent PDEs

MSC codes

  1. 35R15
  2. 60H30
  3. 91G20
  4. 91G80

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Acknowledgments.

The authors would like to thank Lukasz Szpruch and Bernhard Hientzsch for stimulating discussions, as well as the referees and the Associate Editor for their insightful comments.

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Information & Authors

Information

Published In

cover image SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
Pages: 353 - 382
ISSN (online): 1945-497X

History

Submitted: 11 June 2019
Accepted: 3 January 2023
Published online: 25 April 2023

Keywords

  1. rough volatility
  2. deep learning
  3. path-dependent PDEs

MSC codes

  1. 35R15
  2. 60H30
  3. 91G20
  4. 91G80

Authors

Affiliations

Department of Mathematics, Imperial College London, London SW7 2BX, UK, and Alan Turing Institute, London NW1 2DB, UK.
Mugad Oumgari
Lloyds Banking Group plc, Commercial Banking, 10 Gresham Street, London, EC2V 7AE, UK.

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