Investigation of Volatility Forecast Errors using Geometric Brownian Motion and GARCH Models in Sector Indices of Tehran Securities Exchange

Subject Areas : Financial Knowledge of Securities Analysis

Ershad  Emami ¹ (Department Financial Management, College of Management & Social Science, Tehran North Branch, Islamic Azad University, Tehran, Iran. Tehran, IRAN,)
Alireza  Heidarzadeh Hanzaei ² (Assistant Prof. Dr. , Department of Financial Management, Tehran North Branch, Islamic Azad University, Tehran-Iran)

Received: 2022-03-03 Accepted : 2022-08-27 Published : 2022-11-22

Keywords: Price Volatility, Forecasting Volatility, Garch model, Geometric Brownian Motion, Sector Indices,

Abstract :

Current study compares forecasting capability of GARCH (1,1) against Geometric Brownian Motion, GBM, model for daily volatility of indices. The question is to study whether accuracy of GBM forecast differ significantly from its comparing model. Our data consists of 5.5 years (2015 – 2019) of daily logarithmic returns from 38 sector indices within Tehran Stock Exchange. The data was split into estimation period (5 years of daily data) and forecast period (daily data of the remaining 6 months). The competing models were estimated using maximum likelihood method and based on moving window approach, in which the length of estimating period was kept fixed, and projections were conducted on a daily basis. Root Mean Square Error, RMSE, approach was employed to measure forecasting error of each model. The one with less error will express more capability in forecasting daily volatility. With only three instances of a precise forecast, GARCH showed a relatively worse performance, in comparison to GBM..

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