Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911729539088384 |
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| author | Mensah, Abigail Anokyewaa Jha, Ayush Mei, Hongwei Wang, Rui Rachev, Svetlozar T. Fabozzi, Frank J. |
| author_facet | Mensah, Abigail Anokyewaa Jha, Ayush Mei, Hongwei Wang, Rui Rachev, Svetlozar T. Fabozzi, Frank J. |
| contents | 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 Lévy-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30562 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence Mensah, Abigail Anokyewaa Jha, Ayush Mei, Hongwei Wang, Rui Rachev, Svetlozar T. Fabozzi, Frank J. Pricing of Securities Econometrics Mathematical Finance 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 Lévy-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. |
| title | Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence |
| topic | Pricing of Securities Econometrics Mathematical Finance |
| url | https://arxiv.org/abs/2605.30562 |