- Volume 26 Issue 3
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Value at Risk with Peaks over Threshold: Comparison Study of Parameter Estimation
Peacks over threshold를 이용한 Value at Risk: 모수추정 방법론의 비교
- Kang, Minjung (Department of Statistics, Korea University) ;
- Kim, Jiyeon (Department of Statistics, Korea University) ;
- Song, Jongwoo (Department of Statistics, Ewha Womans University) ;
- Song, Seongjoo (Department of Statistics, Korea University)
- Received : 2013.04.01
- Accepted : 2013.04.26
- Published : 2013.06.30
The importance of financial risk management has been highlighted after several recent incidences of global financial crisis. One of the issues in financial risk management is how to measure the risk; currently, the most widely used risk measure is the Value at Risk(VaR). We can consider to estimate VaR using extreme value theory if the financial data have heavy tails as the recent market trend. In this paper, we study estimations of VaR using Peaks over Threshold(POT), which is a common method of modeling fat-tailed data using extreme value theory. To use POT, we first estimate parameters of the Generalized Pareto Distribution(GPD). Here, we compare three different methods of estimating parameters of GPD by comparing the performance of the estimated VaR based on KOSPI 5 minute-data. In addition, we simulate data from normal inverse Gaussian distributions and examine two parameter estimation methods of GPD. We find that the recent methods of parameter estimation of GPD work better than the maximum likelihood estimation when the kurtosis of the return distribution of KOSPI is very high and the simulation experiment shows similar results.
Supported by : 한국연구재단
- Barndorff-Nielsen, O. (1997). Normal inverse Gaussian distributions and stochastic volatility, Scandinavian Journal of Statistics, 24, 1-13. https://doi.org/10.1111/1467-9469.t01-1-00045
- Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics, London.
- Coles, S. and Dixon, M. (1999). Likelihood-based inference for extreme value models, Extremes, 2, 5-23.
- Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer.
- Hosking, J. and Wallis, J. (1987). Parameters and quantile estimation for the Generalized Pareto Distribution, Technometrics, 29, 339-349. https://doi.org/10.1080/00401706.1987.10488243
- Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk, 3rd ed., McGraw Hill.
- Juarez, S. and Schucany, W. (2004). Robust and efficient estimation for the Generalized Pareto Distribution, Extremes, 7, 237-251. https://doi.org/10.1007/s10687-005-6475-6
- Singh, V. P. and Guo, H. (1995). Parameter estimation for 3-parameter generalized Pareto distribution by the principle of maximum entropy (POME), Hydrological Sciences, 40, 165-181. 입니다. https://doi.org/10.1080/02626669509491402
- Song, J. and Song, S. (2012). A quantile estimation for massive data with Generalized Pareto Distribution, Computational Statistics and Data Analysis, 56, 143-150. https://doi.org/10.1016/j.csda.2011.06.030
- Zhang, J. (2007). Likelihood moment estimation for the Generalized Pareto Distribution, Australian and New Zealand Journal of Statistics, 49, 69-77. https://doi.org/10.1111/j.1467-842X.2006.00464.x
- Zhang, J. (2010). Improving on estimation for the Generalized Pareto Distribution, Technometrics, 52, 335-339. https://doi.org/10.1198/TECH.2010.09206
- Zhang, J. and Stephens, M.(2009). A new and efficient estimation method for the generalized Pareto distribution, Technometrics, 51, 316-325. https://doi.org/10.1198/tech.2009.08017
- Vector at Risk and alternative Value at Risk vol.29, pp.4, 2016, https://doi.org/10.5351/KJAS.2016.29.4.689