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Reinforcement learning for options on target volatility funds

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  • Roberto Daluiso
  • Emanuele Nastasi
  • Andrea Pallavicini
  • Stefano Polo

Abstract

In this work we deal with the funding costs rising from hedging the risky securities underlying a target volatility strategy (TVS), a portfolio of risky assets and a risk-free one dynamically rebalanced in order to keep the realized volatility of the portfolio on a certain level. The uncertainty in the TVS risky portfolio composition along with the difference in hedging costs for each component requires to solve a control problem to evaluate the option prices. We derive an analytical solution of the problem in the Black and Scholes (BS) scenario. Then we use Reinforcement Learning (RL) techniques to determine the fund composition leading to the most conservative price under the local volatility (LV) model, for which an a priori solution is not available. We show how the performances of the RL agents are compatible with those obtained by applying path-wise the BS analytical strategy to the TVS dynamics, which therefore appears competitive also in the LV scenario.

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  • Roberto Daluiso & Emanuele Nastasi & Andrea Pallavicini & Stefano Polo, 2021. "Reinforcement learning for options on target volatility funds," Papers 2112.01841, arXiv.org.
    • Handle: RePEc:arx:papers:2112.01841
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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Giuseppe Di Graziano & Lorenzo Torricelli, 2012. "Target Volatility Option Pricing," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 8, pages 207-223, World Scientific Publishing Co. Pte. Ltd..
    3. Martino Grasselli & Jacinto Marabel Romo, 2016. "Stochastic Skew and Target Volatility Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(2), pages 174-193, February.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Giuseppe Di Graziano & Lorenzo Torricelli, 2012. "Target Volatility Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-17.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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