Page 137 - Contributed Paper Session (CPS) - Volume 5

CPS1145 Adeniji Oyebimpe Emmanuel et al.
specification which reduces the number of estimated parameters from infinity
to two. Both the ARCH and GARCH models capture volatility clustering and
Leptokurtosis, but as their distribution is symmetric. They fail to model the
leverage effect. To address this problem, many nonlinear extensions of GARCH
have been proposed, such as the Exponential GARCH (EGARCH) model by
Nelson (1991), the so-called GJR model by Glosten et al (1993) and the
Asymmetric Power ARCH (APARCH) model by Ding et al (1993).
Another problem encountered when using GARCH models is that they do
not always fully embrace the thick tails property of high frequency financial
times series. To overcome this drawback Bollerslev (1987), Baille and Bollerslev
(1987) and Beine et al (2002) have used the Student’s t-distribution. Similarly
to capture skewness Liu and Brorsen (1995) used an asymmetric stable density.
To model both skewness and kurtosis Fernandez and Steel (1998) used the
skewed Student’s t-distribution which was later extended to the GARCH
framework by Lambert and Laurent (2000, 2001). To improve the fit of GARCH
and EGARCH models into international markets, Harris et all (2004) used the
skewed generalised Student’s t-distribution to capture the skewness and
leverage effects of daily returns.
The Beta probalility distribution missed with the student- t distribution and
the resulting mixed- distribution applied to the GARCH model, with little
modification to obtain the volatility model that is robust in modelling jumps.
The Oil and stock markets stress of 1987 and 2008-2009, respectively are good
examples of jumps in volatility series (see Bates, 2000, Pan, 2002). Eraker,
Johnannes and Polson (2003) apply continuous time stochastic volatility
models with jumps components in returns and volatility of S&P500 and
Nasdaq stocks indices ad observe significant evidence of jumps components,
both in the volatility and in the returns. Generalized Autoregressive Score
(GAS), the Exponential GAS (EGAS) and the Asymmetric Exponential GAS
(AEGAS) are new classes of volatility models that simultaneously account for
jumps and asymmetry.
These jumps in ASI were experience as a result of influence of news, politics
and global crisis on Nigeria economy. This project seek to estimate volatility
in the Nigeria Stock Market along with forecasting performance of GARCH and
new classes of volatility models that simultaneously account for jumps and
asymmetry together with different density functions and recommending the
most robust model for financial analysts and portfolio managers in the finance
market. These jumps in ASI were experience as a result of influence of news,
politics and global crisis on Nigeria economy.

DATA SOURCE: A daily data of the All Share Index (ASL) from the period
January 3, 2000 to December 22, 2017 were obtained from CBN statistical
bulletin 2018.

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