An analytical approximation of European option prices under a hybrid GARCH-Vasicek model with double exponential jump in the bid-ask price economy

Shoude Huang; Xinjiang He; Shuqu Qian; Shoude Huang; Xinjiang He; Shuqu Qian

doi:10.3934/math.2024579

AIMS Mathematics

2024, Volume 9, Issue 5: 11833-11850. doi: 10.3934/math.2024579

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Research article

An analytical approximation of European option prices under a hybrid GARCH-Vasicek model with double exponential jump in the bid-ask price economy

1.
School of Mathematics and Computer Science, Anshun University, Guizhou, China
2.
School of Economics, Zhejiang University of Technology, Hangzhou, China
3.
Institute for Industrial System Modernization, Zhejiang University of Technology, Hangzhou, China

Received: 05 January 2024 Revised: 13 March 2023 Accepted: 15 March 2023 Published: 26 March 2024
MSC : 91G20

Conic finance theory, which has been developed over the past decade, replaces classical one-price theory with the bid-ask price economy in option pricing since the one-price principle ignores the bid-ask spread created by market liquidity. Within this framework, we investigate the European option pricing problem when stochastic interest rate, stochastic volatility, and double exponential jump are all taken into account. We show that the corresponding bid and ask prices can be formulated into a semi-analytical form with the Fourier-cosine method once the solution to the characteristic function is obtained. Some interesting properties regarding the new results are displayed via numerical implementation.
- European option,
- Fourier-cosine method,
- bid-ask prices,
- double exponential jump
Citation: Shoude Huang, Xinjiang He, Shuqu Qian. An analytical approximation of European option prices under a hybrid GARCH-Vasicek model with double exponential jump in the bid-ask price economy[J]. AIMS Mathematics, 2024, 9(5): 11833-11850. doi: 10.3934/math.2024579

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Abstract

Conic finance theory, which has been developed over the past decade, replaces classical one-price theory with the bid-ask price economy in option pricing since the one-price principle ignores the bid-ask spread created by market liquidity. Within this framework, we investigate the European option pricing problem when stochastic interest rate, stochastic volatility, and double exponential jump are all taken into account. We show that the corresponding bid and ask prices can be formulated into a semi-analytical form with the Fourier-cosine method once the solution to the characteristic function is obtained. Some interesting properties regarding the new results are displayed via numerical implementation.

References

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