Variety of double knock out barrier option for sustainable financial management

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

Options are financial contracts that are based on an underlying security and are useful for both hedging and speculating on future market trends. New financial tools are constantly being developed for sustainable financial management. In order to define new financial instruments, the BS Hamiltonian, in conjunction with a potential function, is particularly important for modelling path-dependent options. It is demonstrated here how supersymmetry provides a natural framework for generating various options, particularly using higher order supersymmetry to find and examine numerous isospectral partners of the double knock out barrier option.

Keywords

resource management / sustainability / higher order supersymmetry / Black-Scholes hamiltonians / double knock out barrier potential / option Pricing

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] Elkington J (1998) Accounting for the Triple Bottom Line. Measuring Business Excellence 2: 18-22. http://dx.doi.org/10.1108/eb025539

[2] Arowoshegbe AO, Emmanuel U (2016) Sustainability and triple bottom line: an overview of two interrelated concepts. Igbinedion University Journal of Accounting 2: 88-126.

[3] Alhaddi H (2015) Triple bottom line and sustainability: a literature review. Business and Management Studies 2: 6-10. https://doi:10.11114/bms.v1i2.752

[4] Zhang S, Yang Z, Wang S (2020) Design of green bonds by double-barrier options. Discrete and continuous dynamical systems series s 13: 1867-11882. https://doi:10.3934/dcdss.2020110

[5] Sarkar B, Ullah M, Sarkar M (2022) Environmental and economic sustainability through innovative green products by remanufacturing. Journal of Cleaner Production 332: 129813. https://doi.org/10.1016/j.jclepro.2021.129813

[6] AlArjani A, Modibbo MU, Ali I, et al. (2021) A new framework for the sustainable development goals of Saudi Arabia. Journal of King Saud University-Science 33: 101477. https://doi.org/10.1016/j.jksus.2021.101477

[7] Sun S, Ertz M (2022) Can shared micromobility programs reduce greenhouse gas emissions: Evidence from urban transportation big data. Sustainable Cities and Society 85: 104045. https://doi.org/10.1016/j.scs.2022.104045

[8] Hosseini R, Tajik S, Lai KZ, et al. (2022) Quantum Bohmian Inspired Potential to Model Non-Gaussian Events and the Application in Financial Markets. arXiv:2204.11203v1. https://doi.org/10.48550/arXiv.2204.11203

[9] Ramos-Calderer S, Prez-Salinas A, Garca-Martn D, et al. (2021) Quantum unary approach to option pricing. Phys Rev A 103: 032414. https://doi.org/10.1103/PhysRevA.103.032414

[10] Orrell D (2020) A quantum model of supply and demand. Physica A 539: 122928. https://doi.org/10.1016/j.physa.2019.122928

[11] Orrell D (2021) A quantum walk model of financial options. Physica A 112: 62-69. https://doi.org/10.1002/wilm.10918

[12] Haven E (2003) A Black-Scholes Schrodinger Option Price: bit versus qubit. Physica A 324: 201-206. https://doi.org/10.1016/S0378-4371(02)01846-0

[13] Haven E (2002) A Discussion on Embedding the Black-Scholes Option Pricing Model in a Quantum Physics Setting. Physica A 304: 507-524. https://doi.org/10.1016/S0378-4371(01)00568-4

[14] Ahn K, Choi YM, Dai B, et al. (2017) Modeling stock return distributions with a quantum harmonic oscillator. Europhysics Letters 120: 38003. https://doi.org/10.1209/0295-5075/120/38003

[15] Chen Q, Guo C (2022) Path Integral Method for Proportional Double-Barrier Step Option Pricing. arXiv 2112: 09534. https://doi.org/10.48550/arXiv.2112.09534

[16] Radha SK (2021) Quantum option pricing using Wick rotated imaginary time evolution. arXiv 2101: 04280. https://doi.org/10.48550/arXiv.2101.04280

[17] Baaquie BE (2004) Quantum finance, Contributions to Nonlinear Functional Analysis , Cambridge University Press.

[18] Schaden M (2002) Quantum finance. Physica A: Statistical Mechanics and its Applications 316: 511-538. https://doi.org/10.1016/S0378-4371(02)01200-1

[19] Ilinski K (2001) Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing. Contributions to Nonlinear Functional Analysis, Wiley.

[20] Baaquie BE (2007) Quantum finance: Path integrals and Hamiltonians for options and interest rates, Contributions to Nonlinear Functional Analysis, Cambridge University Press.

[21] Hicks W (2019) PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes Equation. Entropy 21: 105. https://doi.org/10.3390/e21020105

[22] Jana TK, Roy P (2011) Supersymmetry in option pricing. Physica A: Statistical Mechanics and its Applications 390: 2350-2355. https://doi.org/10.1016/j.physa.2011.02.027

[23] Halperin I (2022) Non-Equilibrium Skewness, Market Crises, and Option Pricing: Non-Linear Langevin Model of Markets with Supersymmetry. Physica A: Statistical Mechanics and its Applications 594: 127065. https://doi.org/10.1016/j.physa.2022.127065

[24] Bagrov VG, Samsonov BF (1995) Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics. Theo Math Phys 104: 1051-1060. https://doi.org/10.1007/BF02065985

[25] Bagrov VG, Samsonov BF (1997) Darboux transformation of the Schrdinger equation. Phys Part Nucl 28: 374-397. https://doi.org/10.1134/1.953045

[26] Cooper F, Khare A, Sukhatme U (2001) Supersymmetry in Quantum Mechanics, Contributions to Nonlinear Functional Analysis , Singapore: World Scientific.

[27] Fernandez DJ (1997) SUSUSY Quantum Mechanics. Int J Mod Phys A 12: 171-176. https://doi.org/10.1142/S0217751X97000232

[28] Fernandez DJ, Negro J, Nieto LM (2000) Second-order supersymmetric periodic potentials. Physics Letters A 275: 338-349. https://doi.org/10.1016/S0375-9601(00)00591-0

[29] Pursey DL (1987) Mixed procedures for generating families of isospectral Hamiltonians. Phys Rev D 36: 1103. https://doi.org/10.1103/PhysRevD.36.1103

[30] Mielnik B (1984) Factorization method and new potentials with the oscillator spectrum. J Math Phys 25: 3387. https://doi.org/10.1063/1.526108