Modelagem e previsão do risco de mercados com o uso do VaR

Abstract

The purpose of this paper is to identify whether the normality assumption that is used to calculate the Value at Risk (VaR) is valid, or if the Laplace Probability Distribution Function is more appropriate in real markets. Such identification is done through adherence Kolmogorov-Smirnov test (KS). It was observed that Laplace Distribution had better adhesion, in detriment of Normal Distribution. Thus, the VAR was calculated using the Laplace Distribution parameters. The ARIMA time series prediction model (Auto Regressive Integrated Moving Average), applied to the values calculated by the VaR considering the Laplace distribution, was able to model the temporal dynamics of the estimated risk behavior for the state markets. It used the error Average Percentage Absolute (MAPE) as a measure of adequacy of the ARIMA model to the data. The experiments were carried out with 25 indices worldwide, including: BVSP (IBOVESPA - Brazil), CSE (COLOMBO IND ALL SHS - Sri Lanka), DJI (Dow Jones Industrial Average - USA), FCHI IPC - Mexico), N225 (Nikkei 225 - Japan) and XU100.IS (BIST 100 - Turkey). The single index to reject more than 10% of the data when considered Laplace distribution was XU100.IS (BIST 100 - Turkey), obtaining one ASM value of 31.98%, followed by XMI (NYSE ARCA market index MAJOR USA) with a value of 28.59%.