Actuarial pricing of European options under mixed sub-fractional Brownian motion with the Vasicek interest rate

Fangling Ren; Hui Feng; Fangling Ren; Hui Feng

doi:10.3934/math.20251325

AIMS Mathematics

2025, Volume 10, Issue 12: 30162-30185. doi: 10.3934/math.20251325

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Research article

Actuarial pricing of European options under mixed sub-fractional Brownian motion with the Vasicek interest rate

Fangling Ren ^,,
Hui Feng ^,

College of Mathematics and Computer Science, Yan'an University, Shaanxi 716000, China

Received: 05 September 2025 Revised: 28 November 2025 Accepted: 09 December 2025 Published: 24 December 2025
MSC : 60G22, 60J70, 91G20

To better capture the long-term memory, non-stationary increments, self-similarity, and stochastic nature of interest rates in financial markets, we introduce the Vasicek stochastic interest rate model within a mixed sub-fractional Brownian motion framework to study European option pricing. Using actuarial pricing methods, we derived a closed-form solution for European options under this model. Through numerical simulations and empirical analysis, we examined how variables such as the underlying asset's initial price, strike price, maturity time, volatility, Hurst index, and correlation coefficients influence option prices.
- mixed sub-fractional Brownian motion,
- Vasicek stochastic interest rate model,
- option pricing,
- actuarial method
Citation: Fangling Ren, Hui Feng. Actuarial pricing of European options under mixed sub-fractional Brownian motion with the Vasicek interest rate[J]. AIMS Mathematics, 2025, 10(12): 30162-30185. doi: 10.3934/math.20251325

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Abstract

To better capture the long-term memory, non-stationary increments, self-similarity, and stochastic nature of interest rates in financial markets, we introduce the Vasicek stochastic interest rate model within a mixed sub-fractional Brownian motion framework to study European option pricing. Using actuarial pricing methods, we derived a closed-form solution for European options under this model. Through numerical simulations and empirical analysis, we examined how variables such as the underlying asset's initial price, strike price, maturity time, volatility, Hurst index, and correlation coefficients influence option prices.

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