Power-barrier option pricing formulas in uncertain financial market with floating interest rate

Hua Zhao; Yue Xin; Jinwu Gao; Yin Gao; Hua Zhao; Yue Xin; Jinwu Gao; Yin Gao

doi:10.3934/math.20231040

AIMS Mathematics

2023, Volume 8, Issue 9: 20395-20414. doi: 10.3934/math.20231040

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Power-barrier option pricing formulas in uncertain financial market with floating interest rate

Hua Zhao ¹,
Yue Xin ^{2
,
,},
Jinwu Gao ³,
Yin Gao ⁴

1.
School of Business Administration, Chongqing Technology and Business University, Chongqing, 400067, China
2.
School of Mathematics, Renmin University of China, Beijing 100872, China
3.
School of Economics, Ocean University of China, Qingdao 266100, China
4.
College of Science, Beijing Forestry University, Beijing 100083, China

Received: 22 March 2023 Revised: 24 May 2023 Accepted: 29 May 2023 Published: 25 June 2023
MSC : 91G30, 34H05, 91G80

Power-barrier option is a typical exotic option formed by attaching some restrictions to the power option, where the power option evolves from standard European option with the strike price and underlying good price attached to some power. Compared with the ordinary options, power-barrier option can provide investors with stable leverage and premium income. Therefore, power-barrier option is more favored by investors. This paper mainly discusses the pricing problems of power-barrier option in uncertain financial market. The fluctuation of stock price is regarded as an uncertain process and the interest rate is floating. The uncertain differential equation is invoked to simulate this fluctuation in an uncertain environment. Then, the clear pricing formulas of power-barrier option are given. Finally, the corresponding numerical examples and a real data example are put forward to illustrate the method.
- power option,
- barrier option,
- floating interest rate,
- uncertain differential equation,
- option pricing
Citation: Hua Zhao, Yue Xin, Jinwu Gao, Yin Gao. Power-barrier option pricing formulas in uncertain financial market with floating interest rate[J]. AIMS Mathematics, 2023, 8(9): 20395-20414. doi: 10.3934/math.20231040

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Abstract

Power-barrier option is a typical exotic option formed by attaching some restrictions to the power option, where the power option evolves from standard European option with the strike price and underlying good price attached to some power. Compared with the ordinary options, power-barrier option can provide investors with stable leverage and premium income. Therefore, power-barrier option is more favored by investors. This paper mainly discusses the pricing problems of power-barrier option in uncertain financial market. The fluctuation of stock price is regarded as an uncertain process and the interest rate is floating. The uncertain differential equation is invoked to simulate this fluctuation in an uncertain environment. Then, the clear pricing formulas of power-barrier option are given. Finally, the corresponding numerical examples and a real data example are put forward to illustrate the method.

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