Kopula-GARCH yaklaşımıyla döviz kurları portföyünün risk değerlendirmesi

Yıl 2024, Cilt: 17 Sayı: 1, 1 - 13, 30.06.2024

Emre Yıldırım , Mehmet Ali Cengiz

Öz

Bu çalışmada, USD/TRY ve JPY/TRY döviz kurlarından oluşan portföyün kopula-GARCH yaklaşımıyla risk tahmini yapılmaktadır. Bu amaçla, alternatif ağırlıklandırma teknikleri kullanılarak risk tahmin modelleri oluşturulmaktadır. İlgili değişkenler arasındaki bağımlılık, kuyruk bağımlılığı gibi çeşitli bağımlılık yapılarının modellemede esnek bir yöntem sağladığı için kopulalar aracılığıyla modellenmektedir. Kopula-GARCH yaklaşımı çeşitli ağırlıklandırma teknikleri ile birleştirilerek daha iyi bir risk tahmin modeli elde edilmesi amaçlanmaktadır. USD/TRY ve JPY/TRY döviz kurları arasındaki bağımlılığın çalışmada denenen kopulalar arasında Student t kopula ile en iyi şekilde modellendiği belirlenmiştir. Kopula-GARCH yaklaşımı ile üretilen risk tahmin modellerinin klasik yöntemlere göre daha iyi performans göstermiştir. Son olarak, minimum varyans ağırlıkları ile birleştirilen kopula-GARCH yaklaşımına dayalı risk tahmin modelinin, hem risk ölçümlerinin performansı hem de geriye dönük test sonuçları açısından diğer ağırlıklandırma tekniklerine göre daha iyi sonuçlar verdiği sonucuna varılmıştır.

Anahtar Kelimeler

Kopula yaklaşımı, Bağımlılık modelleme, Döviz kuru piyasası, Risk yönetimi

Risk evaluation of exchange rate portfolio based on the copula-GARCH approach

Öz

In this paper, risk estimation for the portfolio consisting of USD/TRY and JPY/TRY exchange rates is performed via the copula-GARCH approach. For this purpose, risk estimation models are created by means of alternative weighting techniques. The dependency between the related variables is modelled through copulas since they provide a flexible method for modelling various dependency structures such as tail dependency. It is aimed to obtain a better risk estimation model by combining the copula-GARCH approach with several weighting techniques. It is decided that the dependency between USD/TRY and JPY/TRY exchange rates is best modeled by Students' t copula among copulas tried in this study. The risk estimation models produced by the copula-GARCH approach outperform classical methods. Finally, it is concluded that the risk estimation model based on the copula-GARCH approach combined with the minimum variance weights gives better results than other weighting techniques in terms of both the performance of the risk measures and the backtesting outcomes.

Anahtar Kelimeler

: Copula approach, Dependence modelling, Exchange rate market, Risk management, Weighting techniques.

Kaynakça

• [1] Sklar, M. (1959). Fonctions de repartition an dimensions et leurs marges. Publ. inst. statist. univ. Paris, 8, 229-231.
• [2] Patton, A. J. (2006). Modelling asymmetric exchange rate dependence. International economic review, 47(2), 527-556.
• [3] Aloui, R., Aïssa, M. S. B., Hammoudeh, S., and Nguyen, D. K. (2014). Dependence and extreme dependence of crude oil and natural gas prices with applications to risk management. Energy Economics, 42, 332-342.
• [4] Yıldırım, E., and Cengiz, M. A. (2018). Dependency between exchange rate and gold price via copula-DCC-GARCH approach. International Journal for Scientific Research and Development, 6(5), 974-978.
• [5] Reboredo, J. C., Tiwari, A. K., and Albulescu, C. T. (2015). An analysis of dependence between Central and Eastern European stock markets. Economic systems, 39(3), 474-490.
• [6] Yıldırım, E., and Cengiz, M. A. (2022). Modeling dependency between industry production and energy market via stochastic copula approach. Communications in Statistics-Simulation and Computation, 1-14.
• [7] Ignatieva, K., and Trück, S. (2016). Modeling spot price dependence in Australian electricity markets with applications to risk management. Computers & Operations Research, 66, 415-433.
• [8] Lu, X. F., Lai, K. K., and Liang, L. (2014). Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model. Annals of operations research, 219(1), 333-357.
• [9] Wu, C. C., Chung, H., and Chang, Y. H. (2012). The economic value of co-movement between oil price and exchange rate using copula-based GARCH models. Energy Economics, 34(1), 270-282.
• [10] Jin, F., Li, J., & Li, G. (2022). Modeling the linkages between Bitcoin, gold, dollar, crude oil, and stock markets: A GARCH-EVT-copula approach. Discrete Dynamics in Nature and Society, 2022.
• [11] Taleblou, R., & Davoudi, M. M. (2020). Calculating Value at Risk: DCC-GARCH-Copula Approach. Iranian Journal of Economic Research, 25(82), 43-82.
• [12] Bruhn, P., & Ernst, D. (2022). Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach. Journal of Risk and Financial Management, 15(8), 346.
• [13] He, Y., & Hamori, S. (2019). Conditional dependence between oil prices and exchange rates in BRICS countries: An application of the copula-GARCH model. Journal of Risk and Financial Management, 12(2), 99.
• [14] Engle, R. F. (1982). A general approach to Lagrange multiplier model diagnostics. Journal of Econometrics, 20(1), 83-104.
• [15] Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327.
• [16] Theodossiov, P. (1998). Financial data and the skewed generalized t distribution. Management Science, 44(12-part-1), 1650-1661.
• [17] Nelsen, R. B. (2007). An introduction to copulas. Springer Science & Business Media.
• [18] Joe, H., and Kurowicka, D. (Eds.). (2011). Dependence modeling: vine copula handbook. World Scientific.
• [19] Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models (Vol. 95, No. 24). Division of Research and Statistics, Division of Monetary Affairs, Federal Reserve Board.
• [20] Christoffersen, P. F. (1998). Evaluating interval forecasts. International economic review, 841-862.
• [21] Lopez, J. A. (1998). Methods for evaluating value-at-risk estimates. Economic Policy Review, 4(3)