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The generalized trapezoidal model in financial data analysis

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Manuel Franco

    (University of Murcia, Dept. Statistics and Operations Research)

  • Johan René van Dorp

    (The George Washington University, Dept. Engineering Management and Systems Engineering)

  • Juana-María Vivo

    (University of Murcia, Dept. Quantitative Methods for Economy)

Abstract

In many practical problems, it is important to consider different distributions that could be used to model a data set. In this work, we analyze the generalized trapezoidal (GT) model in financial application. The primary reason for this is that the family of the GT distributions includes models with bounded domain used in risk analysis, and it belongs to the nonparametric class of log-concave densities under determined parametric restrictions. In the literature, one can find several references on the log-concavity and applications with interesting qualitative implications in many areas of economics, actuarial sciences, biology and engineering. Here, we classify the log-concavity of the GT model based on its parameters. We observe that it can be useful in analyzing some data sets, especially a financial market data example is used to illustrate that the GT distribution is better fitting than the symmetric distributions previously considered for this data set. Furthermore, in the particular example, the fitted GT distribution satisfies the log-concavity constraints.

Suggested Citation

  • Manuel Franco & Johan René van Dorp & Juana-María Vivo, 2012. "The generalized trapezoidal model in financial data analysis," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 219-227, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2342-0_26
    DOI: 10.1007/978-88-470-2342-0_26
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