Barrier option pricing with floating interest rate based on uncertain exponential Ornstein–Uhlenbeck model

Shaoling Zhou; Huixin Chai; Xiaosheng Wang; Shaoling Zhou; Huixin Chai; Xiaosheng Wang

doi:10.3934/math.20241261

AIMS Mathematics

2024, Volume 9, Issue 9: 25809-25833. doi: 10.3934/math.20241261

Previous Article Next Article

Research article

Barrier option pricing with floating interest rate based on uncertain exponential Ornstein–Uhlenbeck model

School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China

Received: 17 June 2024 Revised: 20 August 2024 Accepted: 21 August 2024 Published: 05 September 2024
MSC : 91G30, 91G80

A barrier option is a kind of path-dependent option whose return depends on whether the price of the underlying asset reaches a certain barrier level. This paper mainly analyzes European barrier option pricing formulas for the uncertain exponential Ornstein–Uhlenbeck model with a floating interest rate. The corresponding numerical algorithms for the knock-in and knock-out option prices are designed. Several numerical examples are given to study the relationship between barrier option prices and parameters. Finally, a real-data example is presented to illustrate the option pricing formulas.
- barrier option,
- exponential Ornstein–Uhlenbeck model,
- floating interest rate,
- option pricing,
- uncertain finance
Citation: Shaoling Zhou, Huixin Chai, Xiaosheng Wang. Barrier option pricing with floating interest rate based on uncertain exponential Ornstein–Uhlenbeck model[J]. AIMS Mathematics, 2024, 9(9): 25809-25833. doi: 10.3934/math.20241261

Related Papers:

Abstract

A barrier option is a kind of path-dependent option whose return depends on whether the price of the underlying asset reaches a certain barrier level. This paper mainly analyzes European barrier option pricing formulas for the uncertain exponential Ornstein–Uhlenbeck model with a floating interest rate. The corresponding numerical algorithms for the knock-in and knock-out option prices are designed. Several numerical examples are given to study the relationship between barrier option prices and parameters. Finally, a real-data example is presented to illustrate the option pricing formulas.

References

[1]	R. C. Merton, Theory of rational option pricing, Bell J. Econ. Manage. Sci., 4 (1973), 141–183. https://doi.org/10.2307/3003143 doi: 10.2307/3003143
[2]	P. Lévy, Sur certains processus stochastiques homogénes, Comp. Math., 7 (1940), 283–339.
[3]	R. C. Heynen, H. M. Kat, Partial barrier options, J. Financ. Eng., 3 (1994), 253–274.
[4]	P. Carr, Two extensions to barrier option valuation, Appl. Math. Financ., 2 (1995), 173–209. https://doi.org/10.1080/13504869500000010 doi: 10.1080/13504869500000010
[5]	N. Kunitomo, M. Ikeda, Pricing options with curved boundaries, Math. Financ., 2 (1992), 275–297. https://doi.org/10.1111/j.1467-9965.1992.tb00033.x doi: 10.1111/j.1467-9965.1992.tb00033.x
[6]	G. F. Armstrong, Valuation formulae for window barrier options, Appl. Math. Financ., 8 (2001), 197–208. https://doi.org/10.1080/13504860210124607 doi: 10.1080/13504860210124607
[7]	T. Guillaume, valuation of options on joint minima and maxima, Appl. Math. Financ., 8 (2001), 209–233. https://doi.org/10.1080/13504860210122384 doi: 10.1080/13504860210122384
[8]	B. Liu, Toward uncertain finance theory, J. Uncertain. Anal. Appl., 1 (2013), 1. https://doi.org/10.1186/2195-5468-1-1 doi: 10.1186/2195-5468-1-1
[9]	B. Liu, Uncertainty theory, 2 Eds., Berlin: Springer-Verlag, 2007. https://doi.org/10.1007/978-3-662-44354-5
[10]	B. Liu, Uncertainty theory: a branch of mathematics for modeling human uncertainty, Berlin: Springer-Verlag, 2010. https://doi.org/10.1007/978-3-642-13959-8
[11]	B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst., 3 (2009), 3–10.
[12]	J. Peng, K. Yao, A new option pricing model for stocks in uncertainty markets, Int. J. Oper. Res., 8 (2011), 18–26.
[13]	X. Chen, Y. Liu, D. A. Ralescu, Uncertain stock model with periodic dividends, Fuzzy Optim. Decis. Making, 12 (2013), 111–123. https://doi.org/10.1007/s10700-012-9141-x doi: 10.1007/s10700-012-9141-x
[14]	Y. Liu, X. Chen, D. A. Ralescu, Uncertain currency model and currency option pricing, Int. J. Intell. Syst., 30 (2015), 40–51. https://doi.org/10.1002/int.21680 doi: 10.1002/int.21680
[15]	J. Deng, Z. Qin, On Parisian option pricing for uncertain currency model, Chaos Soliton. Fract., 143 (2021), 110561. https://doi.org/10.1016/j.chaos.2020.110561 doi: 10.1016/j.chaos.2020.110561
[16]	H. Liu, Y. Zhu, Y. Liu, European option pricing problem based on a class of Caputo-Hadamard uncertain fractional differential equation, AIMS Math., 8 (2023), 15633–15650. https://doi.org/10.3934/math.2023798 doi: 10.3934/math.2023798
[17]	Z. Pan, Y. Gao, L. Yuan, Bermudan options pricing formulas in uncertain financial markets, Chaos Soliton. Fract., 152 (2021), 111327. https://doi.org/10.1016/j.chaos.2021.111327 doi: 10.1016/j.chaos.2021.111327
[18]	K. Yao, Z. Qin, Barrier option pricing formulas of an uncertain stock model, Fuzzy Optim. Decis. Making, 20 (2021), 81–100. https://doi.org/10.1007/s10700-020-09333-w doi: 10.1007/s10700-020-09333-w
[19]	X. Yang, Z. Zhang, X. Gao, Asian-barrier option pricing formulas of uncertain financial market, Chaos Soliton. Fract., 123 (2019), 79–86. https://doi.org/10.1016/j.chaos.2019.03.037 doi: 10.1016/j.chaos.2019.03.037
[20]	R. Gao, K. Liu, Z. Li, R. Lv, American barrier option pricing formulas for stock model in uncertain environment, IEEE Access, 7 (2019), 97846–97856. https://doi.org/10.1109/ACCESS.2019.2928029 doi: 10.1109/ACCESS.2019.2928029
[21]	L. Dai, Z. Fu, Z. Huang, Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model, J. Intell. Manuf., 28 (2017), 597–604. https://doi.org/10.1007/s10845-014-1017-1 doi: 10.1007/s10845-014-1017-1
[22]	Y. Liu, W. Lio, Power option pricing problem of uncertain exponential Ornstein–Uhlenbeck model, Chaos Soliton. Fract., 178 (2024), 114293. https://doi.org/10.1016/j.chaos.2023.114293 doi: 10.1016/j.chaos.2023.114293
[23]	Y. Gao, X. Yang, Z. Fu, Lookback option pricing problem of uncertain exponential Ornstein–Uhlenbeck model, Soft Comput., 22 (2018), 5647–5654. https://doi.org/10.1007/s00500-017-2558-y doi: 10.1007/s00500-017-2558-y
[24]	K. Yao, X. Chen, A numerical method for solving uncertain differential equations, J. Intell. Fuzzy Syst., 25 (2013), 825–832. https://doi.org/10.3233/IFS-120688 doi: 10.3233/IFS-120688
[25]	Y. Sun, T. Su, Mean-reverting stock model with floating interest rate in uncertain environment, Fuzzy Optim. Decis. Making, 16 (2017), 235–255. https://doi.org/10.1007/s10700-016-9247-7 doi: 10.1007/s10700-016-9247-7
[26]	Z. Liu, Asion option pricing formulas based on the uncertain exponential Ornstein–Uhlenbeck model with floating interest rate, Oper. Res. Manage. Sci., 31 (2022), 205–208.
[27]	K. Yao, B. Liu, Parameter estimation in uncertain differential equations, Fuzzy Optim. Decis. Making, 19 (2020), 1–12. https://doi.org/10.1007/s10700-019-09310-y doi: 10.1007/s10700-019-09310-y
[28]	G. Zhang, Y. Shi, Y. Sheng, Uncertain hypothesis testing and its application, Soft Comput., 27 (2023), 2357–2367. https://doi.org/10.1007/s00500-022-07748-8 doi: 10.1007/s00500-022-07748-8

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)