Goodness-of-Fit Assessment of Various Probability Distributions for Interest Rate and Credit Spread Increments in the Russian Market
Abstract
The study is aimed at identifying the theoretical distribution function that best approximates empirical data on interest rate and credit spread increments and provides maximum accuracy in market risk assessment using GARCH-VaR models. The study analyzes the goodness-of-fit of 19 different probability distributions to the empirical distribution of interest rate, bond yield and credit spread increments in the Russian market by using the parametric bootstrap-based Anderson–Darling test and compares VaR models for forecasting quantiles of risk factor increments. To account for the time-varying nature of volatility, the GARCH–X model is applied, which reflects the nonlinear dependence of the volatility of interest rate increments on the level of interest rates. According to the results of the unconditional and conditional coverage tests, the generalized hyperbolic distribution provides the highest accuracy of out-of-sample forecasts among the parametric models. The semi-parametric FHS model, which is simpler in terms of specification and estimation procedures, demonstrates comparable forecast quality. Based on the results obtained, recommendations are formulated for estimating VaR for bonds and fixed income derivatives.
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