An upwind finite difference method for a nonlinear Black–Scholes equation governing European option valuation under transaction costs

Lesmana, Donny Citra; Wang, Song

doi:10.1016/j.amc.2012.12.077

Cited by 45 publications

(44 citation statements)

References 20 publications

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“…The transformed American call option pricing problem under Barles and Soner's model (14)- (20) with parameters (56) and a = 0.05 is considered. Figure 4 demonstrates the difference between the solutions obtained by both alternatives for fixed h 0 and various k. One can see that the difference presents orders no bigger than O(k) that is the order of approximation of the explicit forward in time scheme (25).…”

Section: A U T H O R ' Smentioning

confidence: 98%

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Moving boundary transformation for American call options with transaction cost: finite difference methods and computing

Egorova

Tan

Chen

et al. 2015

International Journal of Computer Mathematics

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The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden's and Schubert's methods are applied as a modification to Newton's method in the case of nonlinearity in the equation. An Alternating Direction Explicit (ADE) method with second order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods.

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Section: A U T H O R ' Smentioning

confidence: 98%

“…One way to overcome this difficulty is to present it as a nonlinear complementarity problem (NCP) arising from the discretisation of the free boundary problem. In [15] and [25] the penalty approach is proposed to solve the NCP by approximating it using an algebraic system of nonlinear equations containing a power penalty term.…”

Section: Introductionmentioning

confidence: 99%

Moving boundary transformation for American call options with transaction cost: finite difference methods and computing

Egorova

Tan

Chen

et al. 2015

International Journal of Computer Mathematics

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“…Several numerical approach can be carried out to solve it, including finite difference method, upwind finite difference method and finite volume methods. Upwind finite difference method and finite volume method proved to be a consistent, stable and monotonous [9,10]. Finite difference method with fully implicit discretization method is monotone and converges to the viscosity solution, while the Crank-Nicolson is only monotone conditionally [8].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for option pricing with stochastic volatility model

Mariani

Nugrahani

Lesmana

2016

IOP Conf. Ser.: Earth Environ. Sci.

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Abstract. The option pricing equations derived from stochatic volatility models in finance are often cast in the form of nonlinear partial differential equations. To solve the equations, we used the upwind finite difference scheme for the spatial discretisation and a fully implicit time-stepping scheme. The result of this scheme is a matrix system in the form of an M-Matrix and we proof that the approximate solution converges to the viscosity solution to the equation by showing that the scheme is monotone, consistent and stable. Numerical experiments are implemented to show that the behavior and the order of convergence of upwind finite difference method.

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“…Since the option pricing in a market is dependent on other markets, the multidimensional Black Scholes equation is more efficient than the one dimensional version. There are various methods to find the solution of multidimensional Black Scholes model; for example, a radical basic function (RBF) method [2][3][4][5][6], the Mellin transform method [7], finite different method [8][9][10][11][12], a collection method with the quantic B-spline function [13], and homotopy perturbation method (HPM) [14,15].…”

Section: Introductionmentioning

confidence: 99%

Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

Trachoo

Sawangtong

2017

MCA

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Abstract:The Black Scholes model is a well-known and useful mathematical model in financial markets. In this paper, the two-dimensional Black Scholes equation with European call option is studied. The explicit solution of this problem is carried out in the form of a Mellin-Ross function by using Laplace transform homotopy perturbation method. The solution example demonstrates that the proposed scheme is effective.

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An upwind finite difference method for a nonlinear Black–Scholes equation governing European option valuation under transaction costs

Cited by 45 publications

References 20 publications

Moving boundary transformation for American call options with transaction cost: finite difference methods and computing

Moving boundary transformation for American call options with transaction cost: finite difference methods and computing

Numerical solution for option pricing with stochastic volatility model

Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

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