Value at Risk with Performing Exponential Generalized Autoregressive Conditional Heteroscedasticity–Generalized Pareto Distribution

Nadiyah Hafidah Sinambela; Di Asih I Maruddani; Arief Rachman Hakim

doi:10.19184/jid.v23i1.18822

Nadiyah Hafidah Sinambela Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro
Di Asih I Maruddani Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro
Arief Rachman Hakim Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro

DOI: https://doi.org/10.19184/jid.v23i1.18822

Abstract

Stocks are an investment that many investors are interested in but often have a high risk. Value at Risk (VaR) is one tool that is often used in risk measurement. In general, financial data fluctuate rapidly so that the variants of the residuals are not constant or heteroscedasticity. The condition of heteroscedasticity is modeled using the ARCH/GARCH model. If there is an asymmetric effect on the data, it is modeled using an asymmetric GARCH model, namely Exponential GARCH (EGARCH). In addition to the impacts of heteroscedasticity and asymmetric events, extreme events in fat distribution tails are modeled using the Extreme Value Theory method, namely the Peaks Over Threshold method with the Generalized Pareto Distribution (GPD) approach. The data in this study is the return data of PT. Indocement Tunggal Prakarsa Tbk (INTP) for the period of March 1, 2013 - October 31, 2018. It was found that the data was heteroscedasticity, asymmetric, and there were also fat distribution tails, so it was modeled using a combination of EGARCH-GPD models. ARIMA ([2], 0, [2,13]) EGARCH (1,1) has the smallest AIC compared to other models, and then we choose it as the best model. The amount of risk with a 95% confidence level obtained with the GPD approach is 0.333% of current investment.

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