Detection, modelling and implications of non-normality in financial economics : normal inverse Gaussian modelling of Norwegian stock market returns and consumption growth

摘要

This thesis shows that the Norwegian stock market deviates significantly from what one mightthink 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 observationfrequency (daily, monthly and quarterly) we have investigated in this thesis. More specifically,the return distribution is both leptokurtic and negatively skewed. Secondly, the empirical returndistribution is time-varying; we find both autocorrelation in returns and volatility clustering. Bothof these deviations from the baseline model can potentially have important implications fortheoretical 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 ofsample. Our NIG modelling approach allows us to deviate from the normality assumption, but itis not able to capture the dependencies across time. This model of returns turns out to be useful inrisk measurement, where the baseline model grossly underestimate well-known metrics such asvalue 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-freeinterest rates and the equity premium, suggested by Aase and Lillestøl (2015), in order to explainthe equity premium puzzle. The NIG model allows for fatter tails and negative skewness in thejoint return and consumption distribution, thereby reducing the implied risk aversion parameterand increasing the impatience rate of the representative consumer. Although the model takes us inthe right direction in terms of both implied parameters, the improvement is only slightly morethan negligible and it happens at the cost of a great increase in complexity.