Numerical pricing based on fractional Black–Scholes equation with time-dependent parameters under the CEV model: Double barrier options

Rezaei, Mohammad; Yazdanian, A. R.; Ашрафи, Али Реза; Mahmoudi, Seyed Mahdi

doi:10.1016/j.camwa.2021.02.021

Cited by 23 publications

(19 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the procedure can be used to solve inverse source problem (2) by taking some modifications. Other similar research interesting can be found [7,11,32] and the references therein.…”

Section: Introductionmentioning

confidence: 57%

Solutions of a Time Fractional Black-Scholes Equation Under the Constant Elasticity of Variance Process

Zhang¹

2023

Int. J. of Appl. Math.

View full text Add to dashboard Cite

In this paper we consider backward problem and inverse source problem for time-fractional Black-Scholes equation, which arises from pricing double barrier option under the constant elasticity of variance process. Main tools are spectral method and Sturm-Liouville theory. The existence, uniqueness and convergence analysis of analytic solutions of the backward problem and inverse source problem of time-fractional Black-Scholes model are established in terms of Whittaker functions or modified Bessel functions with large variables.

show abstract

Section: Introductionmentioning

confidence: 57%

Solutions of a Time Fractional Black-Scholes Equation Under the Constant Elasticity of Variance Process

Zhang¹

2023

Int. J. of Appl. Math.

View full text Add to dashboard Cite

show abstract

“…After the fractal structures for the fnancial market [11] were discovered, the standard Brownian motion of the classical Black-Scholes equation was replaced by fractional Brownian motion to obtain the fractional Black-Scholes model. Some such models are the fractional Black-Scholes pricing model on arbitrage and replication [12], tempered fractional Black-Scholes equation for European double barrier option [13], pricing fnancial options model in fractal transmission system [14], fractional Black-Scholes model with stochastic volatility [15], pricing double barrier options in a time-fractional Black-Scholes model [16], fractional Black-Scholes equation under the constant elasticity of variance (CEV) model [17], fractional Black-Scholes model with European option [18], and two-dimensional fractional Black-Scholes equation [19]. A time-space-fractional Black-Scholes European option pricing model [20] arising in the fnancial market is given as…”

Section: Introductionmentioning

confidence: 99%

New Solutions of Time- and Space-Fractional Black–Scholes European Option Pricing Model via Fractional Extension of He-Aboodh Algorithm

Qayyum,

Ahmad

2024

Journal of Mathematics

View full text Add to dashboard Cite

The current study explores the space and time-fractional Black–Scholes European option pricing model that primarily occurs in the financial market. To tackle the complexities associated with solving models in a fractional environment, the Aboodh transform is hybridized with He’s algorithm. This facilitates in improving the efficiency and applicability of the classical homotopy perturbation method (HPM) by ensuring the rapid convergence of the series form solution. Three cases that are time-fractional scenario, space-fractional scenario, and time-space-fractional scenario are observed through graphs and tables. 2D graphical analysis is performed to depict the behaviour of a given option pricing model for varying time, stock price, and fractional parameters. Solutions of the European option pricing model at various fractional orders are also presented as 3D plots. The results obtained through these graphs unfold the interchange between time- and space-fractional derivatives, presenting a comprehensive study of option pricing under fractional dynamics. The competency of the proposed scheme is illustrated via solutions and errors throughout the fractional domain in tabular form. The validity of the He-Aboodh results is exhibited by comparison with existing errors. Analysis shows that the proposed methodology (He-Aboodh algorithm) is a valuable scheme for solving time-space-fractional models arising in business and economics.

show abstract

“…Staelen and Hendy [2] studied an implicit numerical scheme with a temporal accuracy of (2 − α)-order and spatial accuracy of fourth-order by using the Fourier analysis method. In addition, some other related numerical methods based on differential spatial discrezations for the TFBS model can be found in [17][18][19][20][21][22][23][24][25] It is worth noting that the above numerical methods can reach the theoretical convergence order with the assumption that the exact solution of TFBS model is sufficiently smooth in the time variable. But in fact, the solutions of time-fractional differential equations always show weak singularities near the initial time, which makes most of the above numerical methods to achieve optimal order convergence [26,27].…”

Section: Introductionmentioning

confidence: 99%

A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model

Zhou¹,

Gu²,

Shen³

et al. 2023

Preprint

View full text Add to dashboard Cite

The Black-Scholes (B-S) equation has been recently extended as a kind of tempered timefractional B-S equations, which become an interesting mathematical model in option pricing. In this study, we provide a fast numerical method to approximate the solution of the tempered time-fractional B-S model. To achieve high-order accuracy in space and overcome the weak initial singularity of the solution, we combine the compact operator with a tempered L1 approximation with nonuniform time steps to yield the numerical scheme. The convergence of the proposed difference scheme is proved to be unconditionally stable. Moreover, the kernel function in tempered Caputo fractional derivative is approximated by sum-of-exponentials, which leads to a fast unconditional stable compact difference method that reduces the computational cost. Finally, numerical results demonstrate the effectiveness of the proposed methods.

show abstract

Numerical pricing based on fractional Black–Scholes equation with time-dependent parameters under the CEV model: Double barrier options

Cited by 23 publications

References 18 publications

Solutions of a Time Fractional Black-Scholes Equation Under the Constant Elasticity of Variance Process

Solutions of a Time Fractional Black-Scholes Equation Under the Constant Elasticity of Variance Process

New Solutions of Time- and Space-Fractional Black–Scholes European Option Pricing Model via Fractional Extension of He-Aboodh Algorithm

A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model

Contact Info

Product

Resources

About