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Modeling Dependence of Asian Stock Markets Using Dynamic Copula Functions

K. Dharmawan, L. P. Ida Harini, I W. Sumarjaya

Abstract



The aim of this paper is to analyze the time dynamic of the dependence structure between Jakarta Stock Exchange Index (JKSE) and four Asian Indexes, Hang Seng, Nikkei, KOSPI, and Straits Times Index (STI). We set up the dynamic of the dependence structure based on Patton’s formulation. In addition, we observe the effect of tail dependence of different copula functions on VaR estimation. We use AR(1)-GJR(1,1) to fit the margin of each series. Then we apply time-varying Normal Copula, time-varying Rotated Gumbel Copula (RGC), and time-varying Symmetrized-Joe-Clayton Copula (SJC) to model the dependence between the stock indexes. Next, we look for the best copula representing the relation among stock indexes. To do this we apply AIC, BIC, and Log-Likelihood to choose the most representing copula. Our result shows that time-varying Normal and SJC are best fit the pair JKSE-STI, while Normal copula fits better the rest of the pairs. We also calculate VaR and CVaR from the fitted copulas, and conclude that VaR using Normal copula is more aggressive than RGC and SJC. This means that Normal copula gives higher opportunities to investors to gain higher return as they set at a higher risk. Finally, backtesting is carried out to test the accuracy of VaR and CVaR models. The test shows that Normal copula gives lower exceedance than RGC and SJC copula for all portfolios.

Keywords


dependence structure, dynamic copula, value-at-risk, conditional value-at-risk

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