Numerically pricing double barrier options in a time-fractional Black–Scholes model

Staelen, Rob De; Hendy, Ahmed S.

doi:10.1016/j.camwa.2017.06.005

Cited by 84 publications

(44 citation statements)

References 13 publications

(19 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have analysed the solvability, stability, and convergence of the constructed scheme and provided the optimal error estimates. The constructed scheme has the second-order temporal accuracy and the fourth-order spatial accuracy, which improves the temporal accuracy of the method given in [8].…”

Section: Advances In Mathematical Physicsmentioning

confidence: 85%

“…From the table, we can see that the computed solution has the second-order temporal accuracy. For comparison, the corresponding temporal convergence orders O t ] ( , ℎ) (] = ∞) given in [8] has only 2− order; thus it is far less accurate than the compact difference scheme (23) given in this paper.…”

Section: Numerical Experimentsmentioning

confidence: 90%

“…In [7], H.Zhang et al use some numerical technique to price a European doubleknock-out barrier option, and then the characteristics of the three fractional Black-Scholes models are analysed through comparison with the classical Black-Scholes model. More recently, a numerical scheme of fourth-order in space and 2 − in time is derived in [8]; the solvability and convergence of the proposed numerical scheme are proved rigorously using a Fourier analysis. Some computationally efficient numerical methods have been proposed for solving fractional differential equation, for example, which include finite difference methods, finite element methods, finite volume methods, spectral methods, and meshless methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

Ren

Liu

2019

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the L2-1σ approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.

show abstract

Section: Advances In Mathematical Physicsmentioning

confidence: 85%

Section: Numerical Experimentsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

Ren

Liu

2019

Advances in Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…The numerical results in this section confirmed our claim. We then compare the achieved option prices from our scheme with those of [33] and [25] that our method gives better results. In addition, the accuracy and efficiency of the developed method demonstrated that they are obtained by the relation…”

Section: Numerical Investigationmentioning

confidence: 99%

The impact of the Chebyshev collocation method on solutions of the time-fractional Black–Scholes

2020

View full text Add to dashboard Cite

This paper presents a numerical solution of the temporal-fractional Black–Scholes equation governing European options (TFBSE-EO) in the finite domain so that the temporal derivative is the Caputo fractional derivative. For this goal, we firstly use linear interpolation with the $$(2-\alpha)$$ ( 2 - α ) -order in time. Then, the Chebyshev collocation method based on the second kind is used for approximating the spatial derivative terms. Applying the energy method, we prove unconditional stability and convergence order. The precision and efficiency of the presented scheme are illustrated in two examples.

show abstract

“…Therefore, efficient numerical methods become essential. Zhang et al [27] and Staelen and Hendy [7] developed implicit finite difference methods for pricing the barrier options under the Wyss' time-fractional B-S equation. Golbabai and Nikan [8] also proposed a numerical approach based on the moving least-squares method to approximate the Wyss' time-fractional B-S equation for pricing the barrier options.…”

Section: Introductionmentioning

confidence: 99%

An adaptive moving mesh method for a time-fractional Black–Scholes equation

2019

View full text Add to dashboard Cite

In this paper we study the numerical method for a time-fractional Black-Scholes equation, which is used for option pricing. The solution of the fractional-order differential equation may be singular near certain domain boundaries, which leads to numerical difficulty. In order to capture the singular phenomena, a numerical method based on an adaptive moving mesh is developed. A finite difference method is used to discretize the time-fractional Black-Scholes equation and error analysis for the discretization scheme is derived. Then, an adaptive moving mesh based on an a priori error analysis is established by equidistributing monitor function. Numerical experiments support these theoretical results. MSC: 65M06; 65M12; 65M15

show abstract

Numerically pricing double barrier options in a time-fractional Black–Scholes model

Cited by 84 publications

References 13 publications

An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

The impact of the Chebyshev collocation method on solutions of the time-fractional Black–Scholes

An adaptive moving mesh method for a time-fractional Black–Scholes equation

Contact Info

Product

Resources

About