Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

Wang, Jun; Liang, Jing; Lv, Longjin; Qiu, Weiyuan; Ren, Fu-Yao

doi:10.1016/j.physa.2011.09.008

Cited by 32 publications

(24 citation statements)

References 10 publications

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“…Wang et al [8] obtained the modified volatility corresponding to the continuous Black-Scholes equation with transaction cost in subdiffusive regime as…”

Section:  mentioning

confidence: 99%

“…They showed that their model is arbitrage-free. The same idea was used later by Wang et al [8], Hui and Yun-Xiu [9] to obtain a Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime. However, closed-form solutions of these PDEs in finance are generally rare.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we are concerned with the application of the barycentric Jacobi interpolation to value options with transaction costs under fractional [6], mixed Brownian-fractional [10] and subdiffusive fractional [8] Black-Scholes models. Barycentric spectral methods were introduced by Baltensperger et al [11] to solve boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

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Applying the Barycentric Jacobi Spectral Method to Price Options with Transaction Costs in a Fractional Black-Scholes Framework

Nteumagne¹,

Pindza²,

Maré³

2014

JMF

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The aim of this paper is to show how options with transaction costs under fractional, mixed Brownian-fractional, and subdiffusive fractional Black-Scholes models can be efficiently computed by using the barycentric Jacobi spectral method. The reliability of the barycentric Jacobi spectral method for space (asset) direction discretization is demonstrated by solving partial differential equations (PDEs) arising from pricing European options with transaction costs under these models. The discretization of these PDEs in time relies on the implicit Runge-Kutta Radau IIA method. We conducted various numerical experiments and compared our numerical results with existing analytical solutions. It was found that the proposed method is efficient, highly accurate and reliable, and is an alternative to some existing numerical methods for pricing financial options.

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“…Wang et al [8] obtained the modified volatility corresponding to the continuous Black-Scholes equation with transaction cost in subdiffusive regime as…”

Section:  mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Applying the Barycentric Jacobi Spectral Method to Price Options with Transaction Costs in a Fractional Black-Scholes Framework

Nteumagne¹,

Pindza²,

Maré³

2014

JMF

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“…In the last few years, some articles have been published choosing fractional Brownian motion (fBm) as an underlying diffusive process (e.g., Refs. [7][8][9][14][15][16][17] and references therein). For example, Jiang et al [9] proposed a class of stochastic heat equations with first order fractional noises and established the existence and uniqueness of the solution of the equation.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Jiang et al [9] proposed a class of stochastic heat equations with first order fractional noises and established the existence and uniqueness of the solution of the equation. Wang et al [15] studied the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fBm as a model of asset prices. Xiao et al [17] presented a pricing model for equity warrants in a mixed fractional Brownian environment and proposed a hybrid intelligent algorithm to solve the nonlinear optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion

Liang¹,

Zhang²

2017

J. Nonlinear Sci. Appl.

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Design and analysis of a high order computational technique for time‐fractional Black–Scholes model describing option pricing

Roul

2022

Math Methods in App Sciences

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This work deals with the construction and analysis of a high‐order computational scheme for a time‐fractional Black‐Scholes model that governs the European option pricing. The time‐fractional derivative is considered in the sense of Caputo and the L1 − 2 formula is employed to approximate the Caputo temporal‐fractional derivative of order α, where α ∈ (0, 1). A compact difference scheme is designed for discretization of space variable. The convergence of the method is discussed in detail. It is shown that the proposed method has fourth order accuracy in space and false(3−αfalse)−th order accuracy in time. One numerical example with the known exact solution is considered to demonstrate the applicability and accuracy of present numerical scheme. Moreover, the suggested numerical scheme is employed for pricing three European option problems, namely European call option, European double barrier knock‐out option and European put option. The effect of fractional order derivative on option price profile is investigated. Furthermore, the effects of three relevant parameters, namely volatility, strike price and interest rate on the price of European double barrier knock‐out option are investigated. The computational time for the proposed method is provided.

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Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

Cited by 32 publications

References 10 publications

Applying the Barycentric Jacobi Spectral Method to Price Options with Transaction Costs in a Fractional Black-Scholes Framework

Applying the Barycentric Jacobi Spectral Method to Price Options with Transaction Costs in a Fractional Black-Scholes Framework

Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion

Design and analysis of a high order computational technique for time‐fractional Black–Scholes model describing option pricing

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