Estimation of the value at risk using a long-memory GARCH application to JSE Indices.
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Date
2020
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Abstract
Financial data are characterized by stylized facts; this makes it difficult to model
financial assets if these stylized facts are not taken into account. Therefore, the implementation
of accurate risk management tools such as value at risk (VaR), which
is crucial in the management of market risk, becomes a futile exercise. This study
aims to compare the performance of the long-memory GARCH-type models with
heavy-tailed innovations in estimating the value at risk of the All Share Index, the
Mining Index, and the Banking Index. This was achieved by investigating the empirical
properties of the JSE Indices, fitting the FIGARCH, HYGARCH, and FIAPARCH
with the Student’s t-distribution (STD), skewed Student’s t-distribution (SSTD), and
generalized error distribution (GED). The study further estimates VaR for the short
and long-trading positions on the 95th, 99th, and 99,7th quantiles, as well as backtests
the results. The main findings indicate that the JSE All Share index returns is
best captured by the FIGARCH-SSTD model, whereas the JSE Mining Index retuns
most robust model is the FIAPARCH-STD model. For the JSE Banking Index returns,
the FIAPARCH-STD model is predominantly appropriate at most of different
VaR levels. The findings of the study provide a solution to both risk practitioners
and asset managers for better understanding the behaviour of the financial indices’
returns. Finally, this can assist the role players in fastidiously managing risks and
assets’ returns.
Description
Masters Degree. University of KwaZulu-Natal, Durban.