Pricing geometric average Asian options in the mixed sub-fractional Brownian motion environment with Vasicek interest rate model

Xinyi Wang; Chunyu Wang; Xinyi Wang; Chunyu Wang

doi:10.3934/math.20241293

AIMS Mathematics

2024, Volume 9, Issue 10: 26579-26601. doi: 10.3934/math.20241293

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Research article

Pricing geometric average Asian options in the mixed sub-fractional Brownian motion environment with Vasicek interest rate model

Xinyi Wang ^{1
,
,},
Chunyu Wang ²

1.
School of General Education, Nantong Institute of Technology, Nantong 226002, China
2.
School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China

Received: 17 June 2024 Revised: 20 August 2024 Accepted: 04 September 2024 Published: 13 September 2024
MSC : 58J35, 60H10, 91B26

Considering the characteristics of long-range correlations in financial markets, the issue of valuing geometric average Asian options is examined, assuming that the variations of the underlying asset follow the mixed sub-fractional Brownian motion, and the dynamics of short-term interest rate satisfies the mixed sub-fractional Vasicek model. Based on the principle of no arbitrage, the definite solution of PDE of a zero-coupon bond for geometric average Asian options under the circumstance of the mixed sub-fractional is given by the delta hedging technique. The derivation of the explicit pricing formula for geometric average Asian options with fixed strike price is achieved through the utilization of multiple variable substitutions. Furthermore, we perform numerical calculations to analyze the performance of the model.
- option pricing,
- mixed sub-fractional Brownian motion,
- geometric average Asian options,
- Vasicek short rate model
Citation: Xinyi Wang, Chunyu Wang. Pricing geometric average Asian options in the mixed sub-fractional Brownian motion environment with Vasicek interest rate model[J]. AIMS Mathematics, 2024, 9(10): 26579-26601. doi: 10.3934/math.20241293

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Abstract

Considering the characteristics of long-range correlations in financial markets, the issue of valuing geometric average Asian options is examined, assuming that the variations of the underlying asset follow the mixed sub-fractional Brownian motion, and the dynamics of short-term interest rate satisfies the mixed sub-fractional Vasicek model. Based on the principle of no arbitrage, the definite solution of PDE of a zero-coupon bond for geometric average Asian options under the circumstance of the mixed sub-fractional is given by the delta hedging technique. The derivation of the explicit pricing formula for geometric average Asian options with fixed strike price is achieved through the utilization of multiple variable substitutions. Furthermore, we perform numerical calculations to analyze the performance of the model.

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