A spectral approach using fractional Jaiswal functions to solve the mixed time-fractional Black-Scholes European option pricing model with error analysis

Alazemi, Fares; Alsenafi, Abdulaziz; Najafi, Alireza

doi:10.1007/s11075-024-01797-w

Numer Algor

2024

DOI: 10.1007/s11075-024-01797-w

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A spectral approach using fractional Jaiswal functions to solve the mixed time-fractional Black-Scholes European option pricing model with error analysis

Fares Alazemi,

Abdulaziz Alsenafi,

Alireza Najafi

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Cited by 2 publications

References 39 publications

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Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Cai,

Kosari,

Shafi

et al. 2024

Phys. Scr.

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In this manuscript, a new model of the time-fractional Galilei-invariant advection-diffusion model of distributed order is studied. An efficient hybrid numerical approach with high accuracy is used to estimate this equation. The finite difference numerical method is used to approximate the fractional operator in terms of the time variable and to approximate the integral term of distributed order, the Gaussian--Legendre integration is applied. To obtain a fully discrete numerical approach, we used a spectral element numerical approach, in which Legendre polynomials are used as the basis function. For the proposed numerical approach, the error and stability analysis are studied. For the efficiency of the numerical approach, some numerical examples are presented with graphs and tables.

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Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Cai,

Kosari,

Shafi

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Pricing Asian Options in Uncertain Stochastic Markets With Jumps

Chirima,

Matenda,

Sibanda

2024

RGSA

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Objective: In practice, the securities industry is characterized by processes exhibiting both randomness and Liu's uncertainty, sometimes called uncertainty. This study proposes Asian option pricing models in uncertain random markets with jumps. Theoretical Framework: This research is based on the concepts of probability, uncertainty, and uncertain stochastic differential equations (USDEs) with jumps. Method: We use an uncertain random stock model with a jump to derive option pricing models in uncertain random markets with jumps. Using USDEs with jumps is a new paradigm in modeling dynamical systems. The solution to the extraordinary type of an uncertain stochastic differential equation (USDE) with jumps examined in this article combines a jump component and the geometric Itô-Liu process. It plays a pivotal role in deriving Asian option pricing formulae under study. Results and Discussion: This study shows that objective randomness and subjective uncertainty are essential in pricing Asian options. Research Implications: The proposed procedures in this branch of knowledge can be used to price Asian options. Originality/Value: This study contributes to the literature by adequately capturing the effects of indeterminacy in pricing Asian options.

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A spectral approach using fractional Jaiswal functions to solve the mixed time-fractional Black-Scholes European option pricing model with error analysis

Cited by 2 publications

References 39 publications

Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Pricing Asian Options in Uncertain Stochastic Markets With Jumps

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