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Journal of Applied Mathematics
Volume 2007 (2007), Article ID 62098, 8 pages
http://dx.doi.org/10.1155/2007/62098
Research Article

Recovery of Time-Dependent Parameters of a Black-Scholes-Type Equation: An Inverse Stieltjes Moment Approach

1Departamento Académico de Matemáticas, Instituto Tecnológico Autónomo de México, Mexico 14200, D. F., Mexico
2Department of Statistical and Actuarial Sciences, University of Western Ontario, ON, Canada N6A 1Y2

Received 21 February 2007; Revised 22 May 2007; Accepted 13 August 2007

Academic Editor: Wolfgang Schmidt

Copyright © 2007 Marianito R. Rodrigo and Rogemar S. Mamon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show that the problem of recovering the time-dependent parameters of an equation of Black-Scholes type can be formulated as an inverse Stieltjes moment problem. An application to the problem of implied volatility calculation in the case when the model parameters are time varying is provided and results of numerical simulations are presented.