Numerical solutions of Black-Scholes integro-differential equations with convergence analysis | Zendy

Azim Rivaz | Zendy; M. Mohseni Moghadam | Zendy; Samaneh BANI ASADI | Zendy

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Numerical solutions of Black-Scholes integro-differential equations with convergence analysis

Author(s) -

Azim Rivaz,

M. Mohseni Moghadam,

Samaneh BANI ASADI

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1812-89

Subject(s) - mathematics , numerical analysis , ordinary differential equation , convergence (economics) , hermitian matrix , mathematical analysis , numerical methods for ordinary differential equations , norm (philosophy) , differential equation , collocation method , pure mathematics , economics , political science , law , economic growth

Stochastic integro-differential equations are obtained when we consider prices jump in financial modelling. In this paper, these equations are solved numerically by applying the two-dimensional Tau method with ordinary bases. Next, the numerical solutions of the equations above are investigated by the ordinary bases to the Hermitian one. Moreover, we provide an error analysis for the Tau method with ordinary bases. Also, we will prove that the errors of the approximate solutions decay exponentially in weighted ${L^{2}}$-norm. At the end, we will provide some numerical examples which show the efficiency and accuracy of the method.

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