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On the Pricing of American Options under Stochastic Local Volatility and Stochastic Correlation via the RBSDE Framework

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  • Long Teng

Abstract

In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process. We generalize the class of SLV models by incorporating a flexible stochastic correlation structure. To price options within these extended models, we derive the corresponding reflected forward-backward stochastic differential equations (RBSDEs) and employ data-driven numerical methods to solve them for both pricing and hedging purposes. The RBSDE framework enables the modelling of the future evolution of the option price. Furthermore, we conduct a convergence analysis of the proposed numerical method and present numerical experiments that illustrate the performance of the extended models, as well as the accuracy and efficiency of the RBSDE-based approach.

Suggested Citation

  • Long Teng, 2026. "On the Pricing of American Options under Stochastic Local Volatility and Stochastic Correlation via the RBSDE Framework," Papers 2610.01187, arXiv.org.
    • Handle: RePEc:arx:papers:2610.01187
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    1. Bouchard, Bruno & Chassagneux, Jean-François, 2008. "Discrete-time approximation for continuously and discretely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2269-2293, December.
    2. Teng, Long, 2022. "Gradient boosting-based numerical methods for high-dimensional backward stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    3. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.
    4. Jérôme Lelong, 2018. "Dual pricing of American options by Wiener chaos expansion," Post-Print hal-01299819, HAL.
    5. Bin Chen & Cornelis W. Oosterlee & Hans Van Der Weide, 2012. "A Low-Bias Simulation Scheme For The Sabr Stochastic Volatility Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-37.
    6. Jun Ma, 2009. "Pricing Foreign Equity Options with Stochastic Correlation and Volatility," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 303-327, November.
    7. Joost Driessen & Pascal J. Maenhout & Grigory Vilkov, 2009. "The Price of Correlation Risk: Evidence from Equity Options," Journal of Finance, American Finance Association, vol. 64(3), pages 1377-1406, June.
    8. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    9. Jiefei Yang & Guanglian Li, 2024. "A deep primal-dual BSDE method for optimal stopping problems," Papers 2409.06937, arXiv.org.
    10. Ma, Jin & Zhang, Jianfeng, 2005. "Representations and regularities for solutions to BSDEs with reflections," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 539-569, April.
    11. Long Teng & Matthias Ehrhardt & Michael Günther, 2018. "Quanto Pricing In Stochastic Correlation Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-20, August.
    12. Long Teng & Matthias Ehrhardt & Michael Günther, 2016. "On The Heston Model With Stochastic Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-25, September.
    13. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2023. "Deep stochastic optimization in finance," Digital Finance, Springer, vol. 5(1), pages 91-111, March.
    16. Andres Max Reppen & Halil Mete Soner & Valentin Tissot‐Daguette, 2025. "Neural optimal stopping boundary," Mathematical Finance, Wiley Blackwell, vol. 35(2), pages 441-469, April.
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