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The 3/2 Model As A Stochastic Volatility Approximation For A Large-Basket Price-Weighted Index

Author

Listed:
  • BEN HAMBLY

    (Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK)

  • JUOZAS VAICENAVICIUS

    (Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden)

Abstract

We derive large-basket approximations of a price-weighted index whose component prices follow a single sector jump-diffusion model. As the basket size approaches infinity, a suitable average converges to a Black–Scholes model driven by the common factor process. We extend this by considering the behavior of the residual idiosyncratic noise and show that a version of the 3/2 model emerges as a natural stochastic volatility model approximation. This provides a theoretical justification for its use as a model for jointly pricing index and volatility derivatives.

Suggested Citation

  • Ben Hambly & Juozas Vaicenavicius, 2015. "The 3/2 Model As A Stochastic Volatility Approximation For A Large-Basket Price-Weighted Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-25.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:06:n:s0219024915500417
    DOI: 10.1142/S0219024915500417
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    References listed on IDEAS

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    Cited by:

    1. Paolo Dai Pra & Paolo Pigato, 2025. "A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction," Papers 2504.03445, arXiv.org.
    2. Semere Habtemicael & Indranil SenGupta, 2016. "Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-35, December.
    3. Ben Hambly & Nikolaos Kolliopoulos, 2018. "Fast mean-reversion asymptotics for large portfolios of stochastic volatility models," Papers 1811.08808, arXiv.org, revised Feb 2020.
    4. Paolo Dai Pra & Paolo Pigato, 2025. "A Stochastic Volatility Approximation for a Tick-By-Tick Price Model with Mean-Field Interaction," CEIS Research Paper 596, Tor Vergata University, CEIS, revised 08 Apr 2025.
    5. Oliver Pfante & Nils Bertschinger, 2019. "Volatility Inference And Return Dependencies In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-44, May.
    6. Ben Hambly & Nikolaos Kolliopoulos, 2019. "Stochastic PDEs for large portfolios with general mean-reverting volatility processes," Papers 1906.05898, arXiv.org, revised Mar 2024.

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