Mellin Transform Pricing of Binary Options in a PDE-Equivalent Gaussian Diffusion for a Sub-Mixed Fractional Vasicek Model
- 1School of Digital Economy and Management, Suzhou Polytechnic University, Suzhou 215104, China
- 2School of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
Abstract
This paper develops closed-form prices for binary call options in a time-inhomogeneous Gaussian diffusion whose effective volatility and covariance coefficients are motivated by a sub-mixed fractional Vasicek model with H∈(3/4,1). We derive the pricing PDE by delta hedging and establish the equivalent martingale measure, market completeness, and the Feynman–Kac representation within this diffusion. Applying the Mellin transform—with an explicit treatment of the admissible transform strips and of the regularisation of the discontinuous payoffs—we obtain explicit analytical formulae for both cash-or-nothing call (CONC) and asset-or-nothing call (AONC) options. The closed-form formulae are validated independently by a finite-difference solution of the pricing PDE and by Monte Carlo simulation of the equivalent diffusion: the relative errors are below 0.1% with 106 simulated paths, and degenerate cases recover the classical Black–Scholes binary option prices up to machine precision. Within this diffusion, sensitivity analysis shows that the fractional parameter H has a state-dependent but quantitatively modest impact on prices (within about ±1.2% in our benchmark experiments), the effect being strongest for out-of-the-money options.
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BibTeX
@article{xu2026mellin,
title = {{Mellin Transform Pricing of Binary Options in a PDE-Equivalent Gaussian Diffusion for a Sub-Mixed Fractional Vasicek Model}},
author = {Feng Xu and Xiao-Jun Yang},
journal = {Fractal and Fractional},
year = {2026},
month = nov,
doi = {10.3390/fractalfract10110782},
url = {https://www.mdpi.com/2504-3110/10/11/782},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Mellin Transform Pricing of Binary Options in a PDE-Equivalent Gaussian Diffusion for a Sub-Mixed Fractional Vasicek Model
AU - Feng Xu
AU - Xiao-Jun Yang
PY - 2026
DA - 2026/11/08
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110782
UR - https://www.mdpi.com/2504-3110/10/11/782
AB - This paper develops closed-form prices for binary call options in a time-inhomogeneous Gaussian diffusion whose effective volatility and covariance coefficients are motivated by a sub-mixed fractional Vasicek model with H∈(3/4,1). We derive the pricing PDE by delta hedging and establish the equivalent martingale measure, market completeness, and the Feynman–Kac representation within this diffusion. Applying the Mellin transform—with an explicit treatment of the admissible transform strips and of the regularisation of the discontinuous payoffs—we obtain explicit analytical formulae for both cash-or-nothing call (CONC) and asset-or-nothing call (AONC) options. The closed-form formulae are validated independently by a finite-difference solution of the pricing PDE and by Monte Carlo simulation of the equivalent diffusion: the relative errors are below 0.1% with 106 simulated paths, and degenerate cases recover the classical Black–Scholes binary option prices up to machine precision. Within this diffusion, sensitivity analysis shows that the fractional parameter H has a state-dependent but quantitatively modest impact on prices (within about ±1.2% in our benchmark experiments), the effect being strongest for out-of-the-money options.
SN - 2504-3110
ER -