Detection, modelling and implications of non-normality in financial economics : normal inverse Gaussian modelling of Norwegian stock market returns and consumption growth
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- Master Thesis 
This thesis shows that the Norwegian stock market deviates significantly from what one might think of as a baseline model with identically and independently normally distributed returns. Firstly, the stock market return does not seem to be normally distributed over any observation frequency (daily, monthly and quarterly) we have investigated in this thesis. More specifically, the return distribution is both leptokurtic and negatively skewed. Secondly, the empirical return distribution is time-varying; we find both autocorrelation in returns and volatility clustering. Both of these deviations from the baseline model can potentially have important implications for theoretical models and practical applications. In this paper, we will model the return distribution with a normal inverse Gaussian (NIG) distribution, which we indeed find to outperform Gaussian distributions both in- and out of sample. Our NIG modelling approach allows us to deviate from the normality assumption, but it is not able to capture the dependencies across time. This model of returns turns out to be useful in risk measurement, where the baseline model grossly underestimate well-known metrics such as value at risk and expected shortfall the NIG model fits these measures nicely. This thesis also applies a bivariate NIG distribution to a theoretical model of equilibrium risk-free interest rates and the equity premium, suggested by Aase and Lillestøl (2015), in order to explain the equity premium puzzle. The NIG model allows for fatter tails and negative skewness in the joint return and consumption distribution, thereby reducing the implied risk aversion parameter and increasing the impatience rate of the representative consumer. Although the model takes us in the right direction in terms of both implied parameters, the improvement is only slightly more than negligible and it happens at the cost of a great increase in complexity.