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

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

arXiv 28 May 2026 · q-fin.PR

arXiv:2605.30562 · PDF · DOI · OpenAlex · Extracted main text

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 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.

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29
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Carr, Peter and Geman, Hélyette and Madan, Dilip B. and Yor, Marc (2002) The Fine Structure of Asset Returns: An Empirical Investigation1.00074100%
2Merton, Robert C (1976) Option Pricing When Underlying Stock Returns Are Discontinuous1.00054100%
3Aït-Sahalia, Yacine and Jacod, Jean (2009) Testing for Jumps in a Discretely Observed Process0.92843100%
4Cont, Rama and Mancini, Cecilia (2011) Nonparametric Tests for Analyzing the Fine Structure of Price Fluctuations0.92843100%
5Heston, Steven L (1993) A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options0.92843100%
6Bakshi, Gurdip and Cao, Charles and Chen, Zhiwu (1997) Empirical Performance of Alternative Option Pricing Models0.87452100%
7Kou, Steven G (2002) A Jump-Diffusion Model for Option Pricing0.84333100%
8Bates, David S (1996) Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options0.73732100%
9Cont, Rama and Tankov, Peter (2004) Financial Modelling with Jump Processes0.73732100%
10Cont, Rama and Voltchkova, Ekaterina (2005) Integro-Differential Equations for Option Prices in Exponential Lévy Models0.73732100%

Showing the top 10 of 29 scored citations.