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Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures

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  • Alexandre Carbonneau

    (Department of Mathematics and Statistics, Concordia University, Montréal, QC H3G 1M8, Canada)

  • Frédéric Godin

    (Department of Mathematics and Statistics, Concordia University, Montréal, QC H3G 1M8, Canada)

Abstract

The objective is to study the use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives. The ability to move beyond the class of convex risk measures considered in several prior studies provides more flexibility within the pricing scheme. In particular, suitable choices for the risk measure embedded in the ERP framework, such as the semi-mean-square-error (SMSE), are shown herein to alleviate the price inflation phenomenon observed under the tail value at risk-based ERP as documented in previous work. The numerical implementation of non-translation invariant ERP is performed through deep reinforcement learning, where a slight modification is applied to the conventional deep hedging training algorithm so as to enable obtaining a price through a single training run for the two neural networks associated with the respective long and short hedging strategies. The accuracy of the neural network training procedure is shown in simulation experiments not to be materially impacted by such modification of the training algorithm.

Suggested Citation

  • Alexandre Carbonneau & Frédéric Godin, 2023. "Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures," Risks, MDPI, vol. 11(8), pages 1-27, August.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:8:p:140-:d:1208530
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    References listed on IDEAS

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    Cited by:

    1. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Is the difference between deep hedging and delta hedging a statistical arbitrage?," Papers 2407.14736, arXiv.org, revised Oct 2024.
    2. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org.
    3. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.

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