Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?

• Autorzy: Marcin Chlebus

Warianty tytułu

Czy zastosowanie rozkładów lognormalnego, Weibulla lub Gamma może poprawić prognozy wartości narażonej na ryzyko uzyskiwane na podstawie modeli EWS-GARCH?

• Języki publikacji: EN

Abstrakty

EN

Nowadays a common practice of any insurance company is ratemaking, which is defined as the process of classification of the mass risk portfolio into risk groups where the same premium corresponds to each risk. As generalised linear models are usually applied, the process requires the independence between the average value of claims and the number of claims. However, in literature this assumption is called into question. The interest of this paper is to propose the copula-based total claim amount model taking into account an unobservable risk factor in the claim frequency model. This factor, called also as unobserved heterogeneity, is treated as a random variable influencing the number of claims. The goal is to estimate the expected value of the product of two random variables: the average value of claims and the number of claims for a single risk assuming the dependence between the average value of claims and the number of claims for a single risk and the dependence between the number of claims for a single risk and the unobservable risk factor. We give details of the theoretical aspects of the model as well as the empirical example. To acquaint the reader with the model operation, every step of the process of the expected value estimation in described and the R code is available for download, see http://web.ue.katowice.pl/woali/. (original abstract)

W badaniu analizie poddane zostały dwustopniowe modele EWS-GARCH służące do prognozowania wartości narażonej na ryzyko. W ramach analizy rozpatrywane były modele EWS-GARCH zakładające rozkłady lognormalny, Weibulla oraz Gamma w stanie turbulencji oraz modele GARCH(1,1) i GARCH(1,1) z poprawką na rozkład empiryczny w stanie spokoju. Ocena jakości prognoz Value-at-Risk uzyskanych na podstawie wspomnianych modeli została przeprowadzona na podstawie miar adekwatności (wskaźnik przekroczeń, test Kupca, test Christoffersena, test asymptotyczny bezwarunkowego pokrycia oraz kryteria backtestingu określone przez Komitet Bazylejski) oraz analizy funkcji strat (kwadratowa funkcja straty Lopeza, absolutna funkcja straty Abad i Benito, 3 wersja funkcji straty Caporina oraz funkcja nadmiernych kosztów). Uzyskane wyniki wskazują, że modele EWS-GARCH z rozkładem lognormalnym, Weibulla lub Gamma mogą konkurować z modelami EWS-GARCH z rozkładem wykładniczym lub empirycznym. Modele EWS-GARCH z rozkładem lognormalnym, Weibulla lub Gamma są nieco mniej konserwatywne, jednocześnie jednak koszt ich stosowania jest mniejszy niż modeli EWS-GARCH z rozkładem wykładniczym lub empirycznym.

Słowa kluczowe

EN

Value at Risk Analysis; GARCH model; Forecasting; Market risk; Unobserved heterogeneity

PL

Analiza wartości zagrożonej; Model GARCH; Prognozowanie; Ryzyko rynkowe; Nieobserwowalna heterogeniczność

• Czasopismo: Przegląd Statystyczny
• Rocznik: 2016
• Tom: 63
• Numer: z. 3
• Strony: 329--350

Twórcy

autor

Marcin Chlebus

• University of Warsaw, Faculty of Economic Sciences

Bibliografia

• Abad P., Benito S., (2013), A Detailed Comparison Of Value At Risk Estimates, Mathematics and Computers in Simulation, 94, 258-276.
• Abad P., Benito S., López, C., (2014), A Comprehensive Review Of Value At Risk Methodologies, The Spanish Review of Financial Economics, 12 (1), 15-32.
• Alexander C., Lazar E., (2006), Normal Mixture GARCH(1,1): Applications To Exchange Rate Modelling, Journal of Applied Econometrics, 21, 307-336.
• Alexander C., (2008), Market Risk Analysis, John Wiley & Sons, Chichester.
• Allison P., (2005), Logistic Regression Using SAS: Theory And Application, John Wiley & Sons, Cary, NC: SAS Inst.
• Angelidis T., Benos A., Degiannakis S., (2007), A Robust Var Model Under Different Time Periods And Weighting Schemes, Review of Quantitative Finance and Accounting, 28 (2), 187-201.
• Basel Committee on Banking Supervision, (2006), International Convergence of Capital Measurement and Capital Standards. Revised framework. Comprehensive Version., Online access at 16 November 2013.
• Basel Committee on Banking Supervision, (2011), Revisions to the Basel II market risk framework - updated as of 31 December 2010, Online access at 16 November 2013.
• Bollerslev T., (1986), Generalized Autoregressive Conditional Heteroscedasticity, Journal of Econometrics, 31, 307-327.
• Brownlees C. T., Engle R. F., Kelly B. T., (2011), A Practical Guide To Volatility Forecasting Through Calm And Storm, SSRN Electronic Journal SSRN Journal, Online access at 16 November 2013.
• Cai J., (1994), A Markov Model Of Switching-Regime ARCH, Journal of Business Economic Statistics, 12(3), 309-316.
• Caporin M., (2008), Evaluating Value-At-Risk Measures In The Presence Of Long Memory Conditional Volatility, Journal of Risk, 10, 79-110.
• Chan F., Mcaleer M., (2002), Maximum Likelihood Estimation Of STAR and STAR-GARCH Models: Theory And Monte Carlo Evidence, 17 (5), 509-534.
• Chlebus M., (2016a), One-Day Prediction Of State Of Journal Of Applied EconometricsTurbulence For Portfolio. Models For Binary Dependent Variable, Working Papers 2016-01, Faculty of Economic Sciences, University of Warsaw.
• Chlebus M., (2016b), EWS-GARCH: New Regime Switching Approach To Forecast Value-At-Risk, Working Papers 2016-06, Faculty of Economic Sciences, University of Warsaw.
• Degiannakis S., Floros C., Livada A., (2012), Evaluating Value-At-Risk Models Before And After The Financial Crisis Of 2008, Managerial Finance, 38 (4), 436-452.
• Dimitrakopoulos D. N., Kavussanos M. G., Spyrou S. I., (2010), Value At Risk Models For Volatile Emerging Markets Equity Portfolios, The Quarterly Review of Economics and Finance, 50 (4), 515-526.
• Engle R., (2001), GARCH 101: The Use Of ARCH/GARCH Models In Applied Econometrics, Journal of Economic Perspectives, 15 (4), 157-168.
• Engle R., (2004), Risk And Volatility: Econometric Models And Financial Practice, American Economic Review, 94 (3), 405-420.
• Engle R., Manganelli S., (1999), Caviar: Conditional Autoregressive Value At Risk By Regression Quantiles, NBER Working Paper 7341.
• Engle R., Manganelli S., (2001), Value-At-Risk Models In Finance, Frankfurt am Main 2001. On Line (available at Social Science Research Network). Online access at 16 November 2013.
• Gray S. F., (1996), Modeling The Conditional Distribution Of Interest Rates As A Regime-Switching Process, Journal of Financial Economics, 42 (1), 27-62.
• Hamilton J. D., Susmel R., (1994), Autoregressive Conditional Heteroskedasticity And Changes In Regime, Journal of Econometrics, 64 (1-2), 307-333.
• Lopez J. A., (1999), Methods for Evaluating Value-at-Risk Estimates, Federal Reserve Bank of San Francisco Economic Review, 2, 3-17.
• Marcucci J., (2005), Forecasting Stock Market Volatility With Regime-Switching GARCH Model, Studies in Nonlinear Dynamics & Econometrics, 9 (4), 1-55.
• McAleer M., Jiménez-Martin J., Amaral T. P., (2009), Has The Basel II Accord Encouraged Risk Management During The 2008-09 Financial Crisis?, SSRN Electronic Journal SSRN Journal, Online access at 16 November 2013.
• Nelson D., (1991), Conditional Heteroscedasticity In Asset Returns: A New Approach, Econometrica, 59, 347-370.
• Ozun A., Cifter A., Yilmazer S., (2010), Filtered Extreme-Value Theory For Value-At-Risk Estimation: Evidence From Turkey, The Journal of Risk Finance, 11 (2), 164-179.
• Panjer H. H., (2006), Operational Risk: Modeling Analytics, Wiley Interscience, New York.