NIG distribution in modelling stock returns with assumption about stochastic volatility : Estimation of parameters and application to VaR and ETL

University essay from ;

Abstract: We model Normal Inverse Gaussian distributed log-returns with the assumption of stochastic volatility. We consider different methods of parametrization of returns and following the paper of Lindberg, [21] we assume that the volatility is a linear function of the number of trades. In addition to the Lindberg’s paper, we suggest daily stock volumes and amounts as alternative measures of the volatility. As an application of the models, we perform Value-at-Risk and Expected Tail Loss predictions by the Lindberg’s volatility model and by our own suggested model. These applications are new and not described in the literature. For better understanding of our caluclations, programmes and simulations, basic informations and properties about the Normal Inverse Gaussian and Inverse Gaussian distributions are provided. Practical applications of the models are implemented on the Nasdaq-OMX, where we have calculated Value-at-Risk and Expected Tail Loss for the Ericsson B stock data during the period 1999 to 2004.

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