Document Type : Original Article

Author

• Somayeh Fallah

Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

Abstract

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.

Keywords

• Heston stochastic volatility
• Fractional Vasicek process
• Option pricing
• Fourier transform methods