Mathematical Statistics and Actuarial Science

Permanent URI for this community

http://hdl.handle.net/11660/105

Browse

Browsing Mathematical Statistics and Actuarial Science by Subject "ARFIRMA"

Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    Modelling and analysing risk in precious metals
    (University of the Free State, 2018) Chinhamu, Knowledge; Chikobvu, Delson
    The prices of precious metals are volatile and financial market participants are interested in knowing the downside of holding precious metals in their portfolios. Risk management tools such as Value-at-Risk (VaR) are highly dependent on the underlying distributional assumption. Identifying a distribution that may best capture all the aspects of the given financial data can provide immense advantages to both investors and risk managers. In the analysis and modelling of financial returns, there are stylised facts that are observed. These include volatility clustering, heavy-tails, asymmetry, conditional heavy tails and long range dependence (long memory). In this study, we investigated the stylised facts of gold, platinum and silver returns. We thus propose models that are able to capture their empirical features. The models capture extreme tails of profit and loss distributions and improve the estimation of Value-at-Risk (VaR) of precious metal prices returns. Firstly, we evaluate the performance of existing heavy-tailed and flexible distributions in modelling extreme risk for precious metal returns. The heavy-tailed and flexible distributions used are: Generalised Hyperbolic Distributions (GHDs), Generalised Lambda Distribution (GLD), Stable Distribution (SD), Generalised Pareto Distribution (GPD), Generalised Extreme Value Distribution (GEVD), Pearson type-IV Distribution (PIVD), Symmetrical Student-t Distribution (STD) and Skewed Studentt Distribution (SSTD). Secondly, we couple ARMA-GARCH models and ARMAAPARCH models with heavy-tailed and flexible distributions. We fit the models to precious metal returns and evaluate their relative performance in estimating Valueat-Risk (VaR) using a number of conditional assumptions. The proposed models performed favourably when compared with the APARCH models with a Student-t distribution and the APARCH models with a skewed Student-t distribution usually used in the literature. This provides financial analysts with an alternative distributional scheme to be used in economic modelling. Thirdly, because all daily precious metal price returns exhibit volatility clustering, heavy tails, asymmetry and long range dependence, we fit the long-memory GARCH models under the GHDs, the GPD, the GEVD, the SD, the STD, the SSTD, the GLD and the PIVD assumptions to our price return data. The Anderson-Darling test is used to check for model adequacy. Kupiec likelihood ratio tests and Christoffersen conditional coverage tests are also used in this study to evaluate objectively whether VaR model is adequate. The backtesting results confirm that the long-memory GARCH-heavy-tailed models are adequate for improving risk management assessments and hedging strategies in the highly volatile metal markets. ARFIMA-HYGARCH, ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with PIVD, Normal-Inverse Gaussian Distribution (NIGD), full GHD, FMKL GLD and Generalised Hyperbolic Student-t Distribution (GHStD) innovations are found to be suitable for VaR estimation of precious metals, thereby providing a good alternative candidate for modelling financial returns.