Zpětné testování modelů odhadu měnového rizika na bázi VaR

Abstract

The aim of this thesis is on the basis of backtesting to assess the quality of the estimate Value at Risk at the 99% confidence level by using different models. Estimating the Value at Risk will be determined for the selected exchange rates. Value at Risk is measured through daily returns for a period of seven years. Modeling of returns will be done of using a normal probability distribution models, variance gamma probability distribution and the normal inverse Gaussian probability distribution.Text of this thesis is divided into five chapters. The second chapter aimed on the basic concepts of financial risk management, which defines the individual financial risks, describes the Value at Risk and includes basic methods for calculating Value at Risk. In the end of this chapter are characterized a probability distribution applied for the determination of the Value at Risk.In the third chapter a particular attention is devoted to the description of backtesting and specific tests which serves to estimate Value at Risk. Selected test are the basic frequency test, Kupiec unconditional test, TUFF test, mixed Kupiec test, Christoffers unconditional test and the Basel traffic light test.The fourth chapter deals with backtests for the estimation of Value at Risk, which are applied on the real data. In chapter are characterized the input data and the input parameters. Following backtesting is performed for the selected probability distributions and in the end of the chapter are compared the resulting values for estimate the Value at Risk achieved by backtests.Based on the calculations, it was found that the accuracy of the estimation of Value at Risk depends on the choice of the probability distribution of exchange rates and also on the length of the moving average. As the least desirable for modeling yields exchange rate model was based on the normal probability distribution. The better resulting values were obtained of using the model based on variance gamma distribution and normal inverse Gaussian probability distribution.