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
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Carr, Peter and Geman, Hélyette and Madan, Dilip B. and Yor, Marc (2002) The Fine Structure of Asset Returns: An Empirical Investigation | 1.000 | 7 | 4 | 100% |
| 2 | Merton, Robert C (1976) Option Pricing When Underlying Stock Returns Are Discontinuous | 1.000 | 5 | 4 | 100% |
| 3 | Aït-Sahalia, Yacine and Jacod, Jean (2009) Testing for Jumps in a Discretely Observed Process | 0.928 | 4 | 3 | 100% |
| 4 | Cont, Rama and Mancini, Cecilia (2011) Nonparametric Tests for Analyzing the Fine Structure of Price Fluctuations | 0.928 | 4 | 3 | 100% |
| 5 | Heston, Steven L (1993) A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options | 0.928 | 4 | 3 | 100% |
| 6 | Bakshi, Gurdip and Cao, Charles and Chen, Zhiwu (1997) Empirical Performance of Alternative Option Pricing Models | 0.874 | 5 | 2 | 100% |
| 7 | Kou, Steven G (2002) A Jump-Diffusion Model for Option Pricing | 0.843 | 3 | 3 | 100% |
| 8 | Bates, David S (1996) Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options | 0.737 | 3 | 2 | 100% |
| 9 | Cont, Rama and Tankov, Peter (2004) Financial Modelling with Jump Processes | 0.737 | 3 | 2 | 100% |
| 10 | Cont, Rama and Voltchkova, Ekaterina (2005) Integro-Differential Equations for Option Prices in Exponential Lévy Models | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 29 scored citations.