NON-CENTRAL MOMENTS OF THE TRUNCATED NORMAL VARIABLE IN FINANCE

Fausto Corradin and Domenico Sartore
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Fausto Corradin: GRETA Associati, San Polo 2605, 30125 Venice, Italy

Annals of Financial Economics (AFE), 2021, vol. 16, issue 04, 1-23

Abstract: This paper computes the Non-central Moments of the Truncated Normal variable, i.e. a Normal constrained to assume values in the interval with bounds that may be finite or infinite. We define two recursive expressions where one can be expressed in closed form. Another closed form is defined using the Lower Incomplete Gamma Function. Moreover, an upper bound for the absolute value of the Non-central Moments is determined. The numerical results of the expressions are compared and the different behavior for high value of the order of the moments is shown. The limitations to the use of Truncated Normal distributions with a lower negative limit regarding financial products are considered. Limitations in the application of Truncated Normal distributions also arise when considering a CRRA utility function.

Keywords: Truncated Normal variable; Non-central Moments; Lower Incomplete Gamma Function (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S2010495221500172

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