IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2605.30562.html

Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence

Author

Listed:
  • Abigail Anokyewaa Mensah
  • Ayush Jha
  • Hongwei Mei
  • Rui Wang
  • Svetlozar T. Rachev
  • Frank J. Fabozzi

Abstract

We develop a partial integro-differential equation (PIDE) framework for option pricing under joint stochastic volatility and jump dynamics, and evaluate its empirical content using the S&P500 index option contracts across three maturities. The framework is derived from the infinitesimal generator of an affine L\'evy-type process and implemented via finite-difference discretization with FFT-based treatment of the nonlocal jump operator. Calibration via GMM reveals that stochastic volatility accounts for the dominant share of pricing improvement, where relative to Black-Scholes, the Heston specification reduces implied-volatility RMSE by 39%. Jump augmentation via either Merton or CGMY specifications yields marginal improvements concentrated at short maturities and in the deep out-of-the-money region. The calibrated CGMY activity index supports a compound-Poisson structure, consistent with high-frequency evidence on S&P500 index returns.

Suggested Citation

  • Abigail Anokyewaa Mensah & Ayush Jha & Hongwei Mei & Rui Wang & Svetlozar T. Rachev & Frank J. Fabozzi, 2026. "Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence," Papers 2605.30562, arXiv.org.
    • Handle: RePEc:arx:papers:2605.30562
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2605.30562
    File Function: Latest version
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2605.30562. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.