# Normality assumption for the log-return of the stock prices

• Volume: 32, Issue: 1-2, page 47-58
• ISSN: 1509-9423

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## Abstract

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The normality of the log-returns for the price of the stocks is one of the most important assumptions in mathematical finance. Usually is assumed that the price dynamics of the stocks are driven by geometric Brownian motion and, in that case, the log-return of the prices are independent and normally distributed. For instance, for the Black-Scholes model and for the Black-Scholes pricing formula [4] this is one of the main assumptions. In this paper we will investigate if this assumption is verified in the real world, that is, for a large number of company stock prices we will test the normality assumption for the log-return of their prices. We will apply the Kolmogorov-Smirnov [10, 5], the Shapiro-Wilks [17, 16] and the Anderson-Darling [1, 2] tests for normality to a wide number of company prices from companies quoted in the Nasdaq composite index.

## How to cite

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Pedro P. Mota. "Normality assumption for the log-return of the stock prices." Discussiones Mathematicae Probability and Statistics 32.1-2 (2012): 47-58. <http://eudml.org/doc/270939>.

@article{PedroP2012,
abstract = {The normality of the log-returns for the price of the stocks is one of the most important assumptions in mathematical finance. Usually is assumed that the price dynamics of the stocks are driven by geometric Brownian motion and, in that case, the log-return of the prices are independent and normally distributed. For instance, for the Black-Scholes model and for the Black-Scholes pricing formula [4] this is one of the main assumptions. In this paper we will investigate if this assumption is verified in the real world, that is, for a large number of company stock prices we will test the normality assumption for the log-return of their prices. We will apply the Kolmogorov-Smirnov [10, 5], the Shapiro-Wilks [17, 16] and the Anderson-Darling [1, 2] tests for normality to a wide number of company prices from companies quoted in the Nasdaq composite index.},
author = {Pedro P. Mota},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Anderson-Darling; Black-Scholes; Geometric Brownian motion; Kolmogorov-Smirnov; Log-return; Normality test; Shapiro-Wilks; Anderson-Darling, Black-Scholes; geometric Brownian motion; log-return; normality test},
language = {eng},
number = {1-2},
pages = {47-58},
title = {Normality assumption for the log-return of the stock prices},
url = {http://eudml.org/doc/270939},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Pedro P. Mota
TI - Normality assumption for the log-return of the stock prices
JO - Discussiones Mathematicae Probability and Statistics
PY - 2012
VL - 32
IS - 1-2
SP - 47
EP - 58
AB - The normality of the log-returns for the price of the stocks is one of the most important assumptions in mathematical finance. Usually is assumed that the price dynamics of the stocks are driven by geometric Brownian motion and, in that case, the log-return of the prices are independent and normally distributed. For instance, for the Black-Scholes model and for the Black-Scholes pricing formula [4] this is one of the main assumptions. In this paper we will investigate if this assumption is verified in the real world, that is, for a large number of company stock prices we will test the normality assumption for the log-return of their prices. We will apply the Kolmogorov-Smirnov [10, 5], the Shapiro-Wilks [17, 16] and the Anderson-Darling [1, 2] tests for normality to a wide number of company prices from companies quoted in the Nasdaq composite index.
LA - eng
KW - Anderson-Darling; Black-Scholes; Geometric Brownian motion; Kolmogorov-Smirnov; Log-return; Normality test; Shapiro-Wilks; Anderson-Darling, Black-Scholes; geometric Brownian motion; log-return; normality test
UR - http://eudml.org/doc/270939
ER -

## References

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