Value-At-Risk Estimates and Capital Requirements for Market Risk Obtained from GARCH Predictive Densities

• Autorzy: Mateusz Pipień
• Języki publikacji: EN

Abstrakty

EN

This paper presents an application of the Bayesian inference in Value-at-Risk (VaR) prediction. As a VaR forecasts we use quantiles of the predictive densities obtained from AR(1)-GARCH(1,1) models (see Osiewalski and Pipień 1999, 2003), with α-Stable or Skewed-t conditional distributions; Pipień (2004a, b). Based on the very simple one-dimensional example of the PLN/USD exchange rate, we present the Value at Risk forecasts obtained from each of the models. Using various testing procedures (see Kupiec 1995 and Lopez 1998 and 1999) we compare the accuracy of the VaR estimates among models. We also present the Bayesian prediction of the minimal capital requirements for market risk according to the rules suggested by the Basle Committee of the Banking Supervision. In particular, we check if the quality of the forecasts of the capital charge for the market risk is sensitive to the type of the conditional distribution in GARCH framework.(original abstract)

W artykule zaprezentowano zastosowanie ujęcia bayesowskiego w prognozie wartości narażonej na ryzyko (ang. Value at Risk; VaR). Jako źródła prognoz VaR rozważono procesy AR-GARCH(1,1) z asymetriami (por. Osiewalski i Pipień 1999, 2003) o warunkowym skośnym-t (M₁) lub α-stabilnym (M₂) rozkładzie prawdopodobieństwa. Na podstawie szeregu czasowego dziennych stóp zmian kursu walutowego PLN/USD dokonano oceny wartości narażonej na ryzyko z wykorzystaniem rozkładów predyktywnych uzyskanych z modeli M₁, oraz M₂. Prognozy VaR porównano ex post pod względem wielu kryteriów proponowanych w literaturze takich, jak test Kupca (1995) oraz analiza funkcji strat; por. Lopez (1998), (1999). Prognozy Value at Risk stanowiły punkt wyjścia w określeniu minimalnych rezerw kapitałowych, związanych z ryzykiem walutowym rozważanego kursu. W pracy prezentujemy różnice w prognozie rezerw ze względu na zmiany w typie rozkładu warunkowego w modelach M₁, oraz M₂. (abstrakt oryginalny)

Słowa kluczowe

EN

VaR method; Currency risk; Bayesian models; GARCH model; Exchange rates

PL

Miernik ryzyka (VaR); Ryzyko walutowe; Modele bayesowskie; Model GARCH; Kurs walutowy

• Czasopismo: Acta Universitatis Lodziensis. Folia Oeconomica
• Rocznik: 2005
• Tom: 190 Macromodels 2004 : Problems of Building and Estimation of Econometic Models
• Strony: 197--218

Twórcy

autor

Mateusz Pipień

• Cracow University of Economics, Poland

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