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A Heston Fractional Vasicek Framework for Option Pricing | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 1، اردیبهشت 2026، صفحه 225-249 اصل مقاله (826.91 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.89115.1231 | ||
| نویسنده | ||
| Somayeh Fallah* | ||
| Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| چکیده | ||
| We develop an option-pricing framework that couples the Heston stochastic volatility model with a fractional Vasicek short-rate process to incorporate long-memory effects in interest rates. Using a regularized semimartingale approximation of fractional Brownian motion and an affine surrogate representation, we derive a tractable pricing PDE and a semi-closed-form characteristic function suitable for Fourier-based valuation. The numerical implementation employs adaptive integration for fast and accurate pricing, and sensitivity analysis highlights the role of the memory parameter $\alpha$, the smoothing term $\varepsilon$, and the short-rate volatility $\sigma_r$. Empirical calibration to S\&P~500 option data demonstrates that the proposed model improves the fit to market prices relative to the classical Heston model, particularly for longer maturities. These results indicate that persistent interest-rate dynamics can materially influence equity option valuation and motivate further development of fractional interest-rate modelling. | ||
| کلیدواژهها | ||
| Heston stochastic volatility؛ Fractional Vasicek process؛ Option pricing؛ Fourier transform methods | ||
| مراجع | ||
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