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An Efficient Calibration Framework for Volatility Derivatives under Rough Volatility with Jumps

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  • Keyuan Wu
  • Tenghan Zhong
  • Yuxuan Ouyang

Abstract

We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform and (i) split the pricing formula into data-independent inte- grals and a market-dependent remainder; (ii) precompute those data-independent integrals with GPU acceleration; and (iii) approximate only the remaining, market-dependent pricing map with a small neural network. We instantiate the workflow on a rough volatility model with tempered-stable jumps tailored to power-type volatility derivatives and calibrate it to VIX options with a global-to-local search. We verify that a pure-jump rough volatility model adequately captures the VIX dynamics, consistent with prior empirical findings, and demonstrate that our calibration method achieves high accuracy and speed.

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  • Keyuan Wu & Tenghan Zhong & Yuxuan Ouyang, 2025. "An Efficient Calibration Framework for Volatility Derivatives under Rough Volatility with Jumps," Papers 2510.19126, arXiv.org.
    • Handle: RePEc:arx:papers:2510.19126
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    References listed on IDEAS

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    1. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
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    3. José Da Fonseca & Wenjun Zhang, 2019. "Volatility of volatility is (also) rough," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(5), pages 600-611, May.
    4. Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2019. "Advanced model calibration on bitcoin options," Digital Finance, Springer, vol. 1(1), pages 117-137, November.
    5. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.
    6. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2021. "Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 11-27, January.
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