Removing non-smoothness in solving Black-Scholes equation using a perturbation method

Putri, Endah R. M.; Mardianto, Lutfi; Hakam, Amirul; Imron, Chairul; Susanto, Hadi

doi:10.1016/j.physleta.2021.127367

Cited by 6 publications

(2 citation statements)

References 20 publications

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“…In the computational adventures for the numerical solutions for the Black-Scholes model, different numerical schemes have been developed [21][22][23][24]. The limitations of the numerical schemes have led to the development of various approximate analytical and hybrid methods [25][26][27][28][29][30][31][32][33][34] which provide series solutions. However, the series solutions provide a non-smooth analytical solution at a single point, i.e., when the exercise or strike price is equal to the stock price [34].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Black-Scholes Model for Pricing Barrier Option using Method of Partial Taylor Series Expansion

Sobamowo

2022

EJMS

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In this work, Black-Scholes differential equation for barrier/traditional option is solved using partial Taylor series expansion method. The developed solutions are in very good agreement with the closed-form solutions of the Black Scholes equation for the powered ML-payoff functions. Also, the analytical solutions of the new method in this present study give the same expressions as the solutions of projected differential equations and homotopy perturbation method as presented in the literature. Moreover, the reliability, speed, accuracy, and ease of application of the proposed method show its potential for wide areas of applications in science, financial mathematics, and engineering.

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Section: Introductionmentioning

confidence: 99%

Analytical Solution of Black-Scholes Model for Pricing Barrier Option using Method of Partial Taylor Series Expansion

Sobamowo

2022

EJMS

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“…Such series solutions methods are very essential and necessary especially when there are considerations of more complicated option pricing problems that do not accept symbolic solutions in simple closed forms. However, the series solutions provide a non-smooth analytical solution at a single point, i.e., when the exercise or strike price is equal to the stock price [33]. Consequently, Sumiati et al [34] developed non-series solutions with partly series solution method for the Black-Scholes second-order partial differential equation using Laplace-Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods

2022

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Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods.

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A General Solution of Black–Scholes Equations on Some Rainbow Options

Hakam,

Putri,

Mardianto

2024

Springer Proceedings in Mathematics &Amp; Statistics

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Removing non-smoothness in solving Black-Scholes equation using a perturbation method

Cited by 6 publications

References 20 publications

Analytical Solution of Black-Scholes Model for Pricing Barrier Option using Method of Partial Taylor Series Expansion

Analytical Solution of Black-Scholes Model for Pricing Barrier Option using Method of Partial Taylor Series Expansion

Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods

A General Solution of Black–Scholes Equations on Some Rainbow Options

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