Algebraic solutions for pricing American put options under the constant elasticity of variance (CEV) model: Application of the Lie group approach

Javaid, Saba; Aziz, Arshad; Aziz, Taha

doi:10.1016/j.jocs.2022.101680

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…As opposed to the Black-Scholes model, that assumes constant volatility. The following stochastic differential equation describes the CEV model with dividend yield [20,36]…”

Section: Preliminariesmentioning

confidence: 99%

“…This particular problem pertains to the free boundary problem within a PDE framework. Saba et al [20] conducts classical Lie symmetry analysis and derives new group invariant solutions examining both general and specific cases of the American put option under the CEV model. Recent literature on the CEV model and its applications in mathematical finance can be found in [31,4,12,25,18,21].…”

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confidence: 99%

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Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

Javaid,

Aziz,

Aziz

2024

DCDS-S

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This study aims to use the classical Lie symmetry algorithm to solve a mathematical model that represents the American put option. The model is based on a constant elasticity of variance (CEV) framework and includes factors like dividend yield. An infinitesimal transformation and symmetry generators are obtained for the governing parabolic (1+1) PDE which is also known as a price equation. Classical symmetries for the Black Scholes, Cox-Ingersoll-Ross, and general CEV models with dividend yield help us understand the mathematical structure of these models and their relationships, enabling us to develop more accurate pricing models and better understand investment risks. Group invariant solutions of governing PDE are obtained by using similarity variables which are evaluated by solving the characteristic equation of the symmetry operator. A graphical representation of solutions with different dividend yields is presented and discussed to identify the new attribute. The results indicate that rising interest rates, volatility, dividends, and expiration time conform to the established trends. The effects of the dividends yield in all three cases show a high premium value.

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“…As opposed to the Black-Scholes model, that assumes constant volatility. The following stochastic differential equation describes the CEV model with dividend yield [20,36]…”

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

Javaid,

Aziz,

Aziz

2024

DCDS-S

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“…Incorporating the perceptual dimensions, the property price related information obtained by fusing smart city infrastructure data and open government data can be geometrically represented by points and vectors in the conceptual space. In our previous work [2], based on the infinitesimal Lie symmetry generators, The invariant solutions are derived from the mathematical model and the general [44]. We described the subgroup structure of special linear groups such as SL(2, R) in linear algebra, which is of degree two over the real number field.…”

Section: Introductionmentioning

confidence: 99%

Continuous Symmetry Analysis of the Effects of City Infrastructures on Invariant Metrics for House Market Volatilities

Lin¹,

Wang²,

Zhong³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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The invariant metrics of the effects of park size and distance to public transportation on housing value volatilities in Boston, Milwaukee, Taipei and Tokyo are investigated. They reveal a Cobb-Douglas-like behavior. The scaleinvariant exponents corresponding to the percentage of a green area (a) are 7.4, 8.41, 14.1 and 15.5 for Boston, Milwaukee, Taipei and Tokyo, respectively, while the corresponding direct distances to the nearest metro station (d) are −5, −5.88, −10 and −10, for Boston, Milwaukee, Taipei and Tokyo, respectively. The multiphysics-based analysis provides a powerful approach for the symmetry characterization of market engineering. The scaling exponent ratio between park area percentages and distances to metro stations is approximately 3/2. The scaling exponent ratio expressed in the perceptual stimuli will remain invariant under group transformation. According to Stevens' power law, the perception-dependent feature spaces for parks and public transportation can be described as two-and three-dimensional conceptual spaces. Based on the prolongation structure of the Schrödinger equation, the SL(2, R) models are used to analyze the house-price volatilities. Consistent with Shepard's law, the rotational group leads to a Gaussian pattern, exhibiting an extension of the special linear group structure by embedding SO(3) ⊗ R(3) in SL(2, R). The influencing factors related to cognitive functioning exhibit substantially different scaleinvariant characteristics corresponding to the complexity of the socio-economic features. Accordingly, the contour shapes of the price volatilities obtained from the group-theoretical analysis not only corroborate the impact of the housing pricing estimation in these cities but also reveal the invariant features of their housing markets are faced with the forthcoming sustainable development of big data technologies and computational urban science research.

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The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model

Jhangeer,

Faridi,

Alshehri

2024

Eur. Phys. J. Plus

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Algebraic solutions for pricing American put options under the constant elasticity of variance (CEV) model: Application of the Lie group approach

Cited by 3 publications

References 33 publications

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

Continuous Symmetry Analysis of the Effects of City Infrastructures on Invariant Metrics for House Market Volatilities

The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model

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