Estimation of Value at Risk by Using GJR-GARCH Copula Based on Block Maxima
DOI:
https://doi.org/10.29244/ijsa.v5i2p405-414Keywords:
copula-based asymmetric, GJR-GARCH, GEV distributed, value at riskAbstract
This paper will discuss the risk estimation of a portfolio based on value at risk (VaR) using a copula-based asymmetric Glosten – Jagannathan – Runkle - Generalized Autoregressive Conditional Heteroskedasticity (GJR-GARCH). There is non-linear correlation for dependent model structure among the variables that lead to the inaccurate VaR estimation so that we use copula functions to model the joint probability of large market movements. Data is GEV distributed. Therefore, we use Block Maxima consisting of fitting an extreme value distribution as a tail distribution to count VaR. The results show VaR can estimate the risk of portfolio return reasonably because the model has captured the data properties. Data volatility can be accommodated by GJR-GARCH, Copula can capture dependence between stocks, and Block maxima can accommodate extreme tail behavior of the data.
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References
Allen, D. E., Singh, A. K., & Powell, R. J. (2011). Extreme market risk-an extreme value theory approach.
Brechmann, E. C., & Czado, C. (2013). Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Statistics & Risk Modeling, 30(4): 307–342.
Di Clemente, A., & Romano, C. (2004). A copula-extreme value theory approach for modelling operational risk. Operational Risk Modelling and Analysis, 189–208.
Huang, C.-K., Chikobvu, D., & Chinhamu, K. (2017). Evaluating risk in precious metal prices with generalised Lambda, generalised Pareto and generalised extreme value distributions. South African Statistical Journal, 51(1): 159–182.
Mancini, L., & Trojani, F. (2011). Robust value at risk prediction. Journal of Financial Econometrics, 9(2): 281–313.
Nelsen, R. B. (2007). An introduction to copulas. Springer Science & Business Media.
Onour, I. (2010). Extreme risk and fat-tails distribution model: empirical analysis. Journal of Money, Investment and Banking, (13).
Ren, F., & Giles, D. E. (2010). Extreme value analysis of daily Canadian crude oil prices. Applied Financial Economics, 20(12): 941–954.
Zhang, H., Zhou, L., Ming, S., Yang, Y., & Zhou, M. (2015). Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula. Sci J Appl Math Stat, 3: 136–143.
