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Derivatives Sensitivities Computation under Heston Model on GPU

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  • Pierre-Antoine Arsaguet
  • Paul Bilokon

Abstract

This report investigates the computation of option Greeks for European and Asian options under the Heston stochastic volatility model on GPU. We first implemented the exact simulation method proposed by Broadie and Kaya and used it as a baseline for precision and speed. We then proposed a novel method for computing Greeks using the Milstein discretisation method on GPU. Our results show that the proposed method provides a speed-up up to 200x compared to the exact simulation implementation and that it can be used for both European and Asian options. However, the accuracy of the GPU method for estimating Rho is inferior to the CPU method. Overall, our study demonstrates the potential of GPU for computing derivatives sensitivies with numerical methods.

Suggested Citation

  • Pierre-Antoine Arsaguet & Paul Bilokon, 2023. "Derivatives Sensitivities Computation under Heston Model on GPU," Papers 2309.10477, arXiv.org.
    • Handle: RePEc:arx:papers:2309.10477
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    References listed on IDEAS

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    1. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    2. Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carol Methods for the Heston Model," Research Paper Series 307, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    4. 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.
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