Abstract:

We consider the problem of managing risk in stock market. The Value at Risk (VaR) metric, a widely reported and accepted measure of financial risk, requires accurate estimation of volatility and a corresponding quantile of the empirical distribution. Current researches usually use GARCH type models with normal distribution. However, in this article a GARCH-jump mixture and an Autoregressive-conditional-Jump-Intensity (ARJI–GARCH) models, are used to describe stock price movement and are compared with standard GARCH model to verify the best VaR forecast model for Nasdaq stock index. Normal and Generalized-Error-Distribution (GED) distributions are adopted to describe the diffusion process and heavy tails. We use the unconditional and conditional coverage tests to evaluate the accuracy of VaR forecasting models. Through the GARCH and Jump methodology, empirical results of Nasdaq stock indices on the period from 1 January 2000 to 28 July 2011 provide evidence of conditional Jump dynamics in Nasdaq returns. Another interesting result is that the Jump Garch and the ARJI models perform GARCH models and that GED distribution is more suitable for high confidence level (99%).