Solución numérica del modelo Black-Scholes
no local por molificación discreta

CARLOS D. ACOSTA^*, FERNÁN C. OSORIO

Universidad Nacional de Colombia, Departamento de Matemática y Estadística, Manizales, Colombia.

Resumen. El objetivo de este artículo es estudiar una aproximación numérica de una ecuación de Black-Scholes no local, haciendo uso de técnicas de molificación discreta y diferencias finitas. Analizamos la estabilidad del esquema numérico propuesto mediante monotonía, y discutimos ejemplos numéricos que ilustran las bondades del método.

Palabras clave: Modelo Black-Scholes, diferencias finitas, molificación discreta.
MSC2010: 65M06, 65M12, 35R09.

Numerical solution of the non-local Black-Scholes
model by means of discrete mollification

Abstract. The objective of this paper is to study a numerical approximation of a non-local Black-Scholes equation, by means of techniques of discrete mollification and finite differences. We analyze stability of the proposed numerical scheme through monotony and show examples that illustrate its capabilities.

Keywords: Black-Scholes, finite differences, discrete mollification.

Texto Completo disponible en PDF

References

[1] Acosta C.D. and Mejía C.E., "A mollification based operator splitting method for convection diffusion equations", Comput. Math. Appl. 59 (2010), No. 4, 1397-1408.

[2] Acosta C.D. and Mejía C.E., "Approximate solution of hyperbolic conservation laws by discrete mollification", Appl. Numer. Math. 59 (2009), No. 9, 2256-2265.

[3] Acosta C.D. and Mejía C.E., "Stabilization of explicit methods for convection diffusion equations by discrete mollification", Comput. Math. Appl. 55 (2008), No. 3, 368-380.

[4] Acosta C.D, Büger R. and Mejía C.E., "Monotone difference schemes stabilized by discrete mollification for strongly degenerate parabolic equations", Numer. Methods Partial Differential Equations. 28 (2012), No. 1, 38-62.

[5] Andreu-Vaillo F., Mazón J.M., Rossi J.D. and Toledo-Melero J.J., Nonlocal diffusion problems, Mathematical Surveys and Monographs, 165, 2010.

[6] Bogoya M. and Gómez C.A., "Modelo discreto para una ecuación de difusión no local", Rev. Colombiana Mat. 47 (2013), No. 1, 83-94.

[7] Bhowmik S.K., "Fast and efficient numerical methods for an extended Black-Scholes model", Comput. Math. Appl. 67 (2014), No. 3, 636-654.

[8] Bhowmik S.K., "Stability and convergence analysis of a one step approximation of a Linear partial integro-differential equation", Numer. Methods Partial Differential Equations. 27 (2011), No. 5, 1179-1200.

[9] Pérez-Llanos M. and Rossi J.D., "Numerical approximations for a nonlocal evolution equation", SIAM J. Numer. Anal. 49 (2011), No. 5, 2103-2123.

^*E-mail: cdacostam@unal.edu.co.
Recibido: 14 de mayo de 2015, Aceptado: 16 de octubre 2015.
Para citar este artículo: C.D. Acosta, F.C. Osorio, Solución numérica del modelo Black-Scholes no local por molificación discreta, Rev. Integr. Temas Mat. 33 (2015), No. 2, 145-160.