Daily and Weekly Geometric Brownian Motion Stock Index Forecasts

Amit Sinha ()
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Amit Sinha: Department of Economics and Finance, Foster College of Business at Bradley University, Peoria, IL 61625, USA

JRFM, 2024, vol. 17, issue 10, 1-22

Abstract: In this manuscript, daily and weekly geometric Brownian motion forecasts are obtained and tested for reliability for three indexes, DJIA, NASDAQ and S&P 500. A twenty-year rolling window is used to estimate the drift and diffusion components, and applied to obtain one-period-ahead geometric Brownian motion index values and associated probabilities. Expected values are estimated by totaling up the product of the index value and its associated probabilities, and test for reliability. The results indicate that geometric Brownian-simulated expected index values estimated using one thousand simulations can be reliable forecasts of the actual index values. Expected values estimated using one or ten simulations are not as reliable, while those obtained using at least one hundred simulations could be useful.

Keywords: stock index; DJIA; S&P 500; NASDAQ; geometric Brownian motion; daily and weekly forecasts; simulation; rolling window; probability; expected value (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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