Additive versus multiplicative parameters - applications in economics and finance

TL;DR

This paper explores the use of geometric parameters in economic and financial models, emphasizing multiplicative approaches over additive ones, with practical examples from stock exchange and treasury bills.

Contribution

It introduces the application of geometric mean and standard deviation in finance, providing estimations for heavy-tailed distributions like lognormal and Pareto.

Findings

Geometric parameters are more natural in multiplicative models.

Empirical examples from Warsaw Stock Exchange and treasury bills.

Estimations for heavy-tailed distributions in finance.

Abstract

In this paper, we pay our attention to geometric parameters and their applications in economics and finance. We discuss the multiplicative models in which a geometric mean and a geometric standard deviation are more natural than arithmetic ones. We give two examples from Warsaw Stock Exchange in 1995--2009 and from a bid of 52-week treasury bills in 1992--2009 in Poland as an illustrative example. For distributions having applications in finance and insurance we give their multiplicative parameters as well as their estimations. We consider, among others, heavy-tailed distributions such as lognormal and Pareto distribution, applied to modelling of large losses.