Analysis Of GARCH And ARM Model

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The three variance equation parameters such as ω, α, and β of GARCH-M model with different error distributions for all subset data were significant at 1% level with correct signs which provide evidence in favor of ARCH and GARCH effect. The significant value of ARCH term (α) implies that past stock price innovation influence on current volatility whereas significant GARCH parameter (β) suggest that current volatility of stock price is influenced by past volatility. For asymmetric models (EGARCH-M and TGARCH-M), almost all of the α coefficient and β coefficient were significant for full sample and three sub-periods but exception was found in TGARCH-M model in pre-debacle and debacle period in which α was insignificant (in GED) for pre-debacle period and β was insignificant and negative (in Gaussian) for debacle period.
The results of GARCH-M model with three error distributions for all subset of data except for pre-debacle period showed that they were nonstationary (i.e., α+ β>1). Similar results were also revealed in EGARCH-M model with three error distribution where non-explosiveness condition (i.e., α+ β<1) was not satisfied. So, parameters were overestimated for both GARCH-M
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First, according to the leverage effect hypothesis proposed by Black (1976), financial leverage amplifies with the declines of the stock prices which contribute to increase the stock price volatility. Since these leverage effects are related or identical to asymmetric volatility, the presence of time-varying risk-return relationship could be reflected by asymmetric volatility. Second, the expected risk-return relationship can also help explain the leverage effect. The stock prices decline with the anticipation of higher risk/volatility which tends to increase expected returns. Since investors are rational and risk-averse, they demand less stock with an increase in volatility, causing a decline in stock

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