Comparison of Numerical Methods on Pricing of European Put Options

Mardianto, Lutfi; Pratama, Aditya Putra; Soemarsono, Annisa Rahmita; Hakam, Amirul; Putri, Endah R. M.

doi:10.12962/j24775401.v5i1.3172

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…An option can be an American option or a European option. An America option is an option which can be exercised at any time until expiration or maturity date while a European option is an option which can be exercised only at a fixed expiration or maturity date [2]. The European option can be of two types, namely, call option and put option.…”

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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show abstract

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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“…An exact solution of the Black Scholes equation has been obtained [1]. There are various methods to obtain an exact solution approach: Finite Difference Method [2], [3], Monte Carlo Method [4], Quintic B-spline collocation approach [5], Adomian Decomposition Method (ADM) [6], [7], Homotopy Perturbation Method (HPM) [8], [9], [10], etc.…”

Section: Introductionmentioning

confidence: 99%