European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

A new chaotic financial system is proposed by considering ethics involvement in a fourdimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integerorder system. A discretization scheme is proposed to calculate numerical solutions of conformable derivative systems. The scheme is illustrated by testing hyperchaos for the system. among interest rates, investments, prices, and savings. Chen [12] presented a fractional form of nonlinear financial system. Wang, Huang and Shen [13] established an uncertain fractional-order form of the financial system. Mircea et al. [14] set up a delayed form of the financial system. Xin, Chen, and Ma [15] proposed a discrete form of financial system. Yu, Cai, and Li [16] extended the

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“…Fractional-order economic systems [18,[76][77][78][79][80] can generalize its integer-order forms [17,81].…”

Section: A Conformable Derivative Hyperchaotic Financial System With mentioning

confidence: 99%

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

et al. 2019

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“…The other definition, which is defined by Yang et al [7] in 2017, is based on the normalized sinc function (NSFDO). Especially in recent years, many important theoretical results and applications have been obtained using an operator which has non-local and non-singular kernel such as the Caputo-Fabrizio, NSFDO and ABO [8][9][10][11][12][13][14][15][16][17][18]. Both of these operators have some illustrative advantages according to the operators defined previously such as Caputo [19] and conformable [20].…”

Section: Yavuzmentioning

confidence: 99%

Characterizations of two different fractional operators without singular kernel

Yavuz

2019

Math. Model. Nat. Phenom.

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In this paper, we analyze the behaviours of two different fractional derivative operators defined in the last decade. One of them is defined with the normalized sinc function (NSF) and the other one is defined with the Mittag-Leffler function (MLF). Both of them have a non-singular kernel. The fractional derivative operator defined with the MLF is developed by Atangana and Baleanu (ABO) in 2016 and the other operator defined with the normalized sinc function (NSFDO) is created by Yang et al. in 2017. These mentioned operators have some advantages to model the real life problems and to solve them. On the other hand, since the Laplace transform (LT) of the ABO can be calculated more easily, it can be preferred to solve linear/nonlinear problems. In this study, we use the perturbation method with coupled the LTs of these operators to analyze their performance in solving some fractional differential equations. Furthermore, by constructing the error analysis, we test the practicability and usefulness of the method.

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“…Adomian Decomposition Method (ADM) with conformal derivative and Modified Homotopy Perturbation Method (MHPM) [14], Multivariate Padé Approximation [15] and ADM [16]. Recently fractional order European Vanilla option pricing model has also been studied by Yavuz and Özdemir [17]. These methods have their particular limits and inadequacies.…”

Section: Introductionmentioning

confidence: 99%

A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE)

Jena

2018

SN Appl. Sci.

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In this manuscript, a new expansion technique namely residual power series method is used for finding the analytical solution of the Fractional Black-Scholes equation with an initial condition for European option pricing problem. The Black-Scholes formula is important for estimating European call and put option on a non-dividend paying stock in particular when it contains time-fractional derivatives. The fractional derivative is defined in Caputo sense. This technique is based on fractional power series expansion. The convergence analysis of the present method is also deliberated. Example problems are given to examine the efficacy of the proposed method. Obtained solutions are compared with exact solutions solved by other techniques which demonstrate that the present method is robust and easy to implement for other fractional problems arising in science and engineering.

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European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

Cited by 100 publications

References 35 publications

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

Characterizations of two different fractional operators without singular kernel

A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE)

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