Numerical solution of linear and nonlinear Black–Scholes option pricing equations

Navarro, Enrique; Pintos, José Ramón; Ponsoda, E.

doi:10.1016/j.camwa.2008.02.010

Cited by 72 publications

(49 citation statements)

References 14 publications

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“…(8) and (9), we consider the vanilla call option with parameter r = 0.04 and σ = 0.2 from [22]. Then k = 2r/σ 2 = 2, so we obtain the Padé approximant as The expansion of the series in Eq.…”

Section: Situation Of S < Ementioning

confidence: 99%

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Özdemir

Yavuz

2017

Acta Phys. Pol. A

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In this study, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem. Padé polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Padé approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Padé approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.

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Section: Situation Of S < Ementioning

confidence: 99%

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Özdemir

Yavuz

2017

Acta Phys. Pol. A

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“…In literature, detailed and extensive work on the importance of (1.2) with respect to exact, analytical, approximate or numerical methods of solutions have been captured [7,8,9,10]. Recently, Vukovic [11], established the interconnectedness of the Schrödinger and the Black-Scholes equations via the tools of quantum physics in the sense of Hamiltonian operator.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of the Ivancevic Option Pricing Model With a Nonzero Adaptive Market Potential

Edeki¹,

Ugbebor²,

'alez-Gaxiola³

2017

Int. J. of Pure and Appl. Math.

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“…Many partial differential equations of fractional order have been studied and solved. For example many researchers studied the existence of solutions of the Black-Scholes model using many methods [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

Khan¹,

Ansari²

2016

GLM

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Numerical solution of linear and nonlinear Black–Scholes option pricing equations

Cited by 72 publications

References 14 publications

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Analytical Solutions of the Ivancevic Option Pricing Model With a Nonzero Adaptive Market Potential

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

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