Application of Stochastic Runge-Kutta Methods for Mixed Fractional Brownian Motion Processes

Karimi, Nader; Shahmoradi, Masoumeh

doi:10.22034/cmde.2025.68151.3287

Application of Stochastic Runge-Kutta Methods for Mixed Fractional Brownian Motion Processes

Articles in Press

Document Type : Research Paper

Authors

Nader Karimi ¹
Masoumeh Shahmoradi ²

¹ Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran.

² Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

10.22034/cmde.2025.68151.3287

Abstract

We develop and analyze a stochastic Runge-Kutta (SRK) method for pricing derivatives when the underlying asset follows a mixed fractional Brownian motion (fBm). From this non‑Markovian process, we re‑derive a Black-Scholes‑type partial differential equation (PDE) and show that the proposed SRK integrator is both mean‑square stable and strongly convergent. Sharp bounds for the stability region and the order of convergence are rigorously proved. Numerical experiments confirm the theory and demonstrate the superior accuracy of the SRK method compared with Euler-Maruyama and Milstein schemes.

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