Analytically pricing European options under a two-factor Heston-Vasicek model with regime switching and stochastic interest rate

Xin-Jiang He; Sha Lin; Xin-Jiang He; Sha Lin

doi:10.3934/math.2026160

AIMS Mathematics

2026, Volume 11, Issue 2: 3986-4007. doi: 10.3934/math.2026160

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Research article

Analytically pricing European options under a two-factor Heston-Vasicek model with regime switching and stochastic interest rate

Xin-Jiang He ^1,2,
Sha Lin ^{3,4
,
,}

1.
School of Economics, Zhejiang University of Technology, Hangzhou, China
2.
Institute for Industrial System Modernization, Zhejiang University of Technology, Hangzhou, China
3.
School of Finance, Zhejiang Gongshang University, Hangzhou, China
4.
School of Tailong Finance, Zhejiang Gongshang University, Hangzhou, China

Received: 14 December 2025 Revised: 22 January 2026 Accepted: 04 February 2026 Published: 09 February 2026
MSC : 91G20

This article establishes a hybrid model by adding into the Heston-Vasicek model an additional regime switching factor, which combines the advantages of the stochastic interest rate, regime switching, and multi-factor stochastic volatility. It assumes a Vasicek stochastic interest rate, and uses two stochastic factors for asset volatility, one of which follows Heston stochastic volatility and another can switch according to a continuous-time Markov chain. Such a setting considers both effects of economic cycles and the correlation between the stock and interest rate, while still ensuring the existence of an analytical solution for European option pricing. We further showed how option prices evolve when varying certain model parameters. An empirical study was also carried out to demonstrate the model performance if it was to be applied in practice.
- Heston-Vasicek model,
- regime switching factor,
- analytical pricing formula,
- European options
Citation: Xin-Jiang He, Sha Lin. Analytically pricing European options under a two-factor Heston-Vasicek model with regime switching and stochastic interest rate[J]. AIMS Mathematics, 2026, 11(2): 3986-4007. doi: 10.3934/math.2026160

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Abstract

This article establishes a hybrid model by adding into the Heston-Vasicek model an additional regime switching factor, which combines the advantages of the stochastic interest rate, regime switching, and multi-factor stochastic volatility. It assumes a Vasicek stochastic interest rate, and uses two stochastic factors for asset volatility, one of which follows Heston stochastic volatility and another can switch according to a continuous-time Markov chain. Such a setting considers both effects of economic cycles and the correlation between the stock and interest rate, while still ensuring the existence of an analytical solution for European option pricing. We further showed how option prices evolve when varying certain model parameters. An empirical study was also carried out to demonstrate the model performance if it was to be applied in practice.

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