Azim RIVAZ, Mahmoud Mohseni MOGHADAM, Samaneh BANIASADI

102111

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

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.
Keywords:

Tau method stochastic integro-differential Black-Scholes equation, European option pricing problem, Hermitian polynomial,

PDF
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
Sayıdaki Diğer Makaleler

Sadjia ABBAD, Hacene BELBACHIR, Benali BENZAGHOU

Urszula BEDNARZ, Ma?gorzata WO?OWIEC-MUSIA?

On positive periodic solutions of second-order semipositone differential equations

Nannan YANG, Fanglei WANG

A short note on some arithmetical properties of the integer part of $\alpha p$

Yildirim AKBAL

Salah Eddine RIHANE, Bernadette FAYE, Florian LUCA, Alain TOGBE

Multiplication alteration by two-cocycles for bialgebras with weak antipode

Jose Nicanor ALONSO ALVAREZ, Jose Manuel FERNANDEZ VILABOA, Ramon GONZALEZ RODRIGUEZ

Khadijah SHARAF

Azim RIVAZ, Mahmoud Mohseni MOGHADAM, Samaneh BANIASADI

Zinovii NYTREBYCH, Oksana MALANCHUK, Volodymyr IL'KIV, Petro PUKACH

Some ergodic properties of multipliers on commutative Banach algebras

Hayri TOPAL, Heybetkulu MUSTAFAYEV