Models of sovereign default: relaxing the normality assumption

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School of Business | Master's thesis
Degree programme
57 + 4
The aim of this research is to estimate the probability of a systemic default crisis by studying two centuries of sovereign default data. This is done by examining the empirical qualities of distributions of recurrent periods of systemic debt crisis in 1820s, 1870s, 1930s, and 1980s. My research seeks to answer the questions: (i) if relaxing the assumption for normally distributed data improves the fit between actual and expected default rates, and if (ii) correlations of past defaults can be used to reduce the risk of a sovereign debt portfolio. The research is motivated by earlier critique on the probability-based Gaussian copula model. The model was built on the notion of normally distributed data (Li, 2000) and instead of past default rates, it estimated risk of default based on credit default swaps (MacKenzie and Spears, 2014). The results of this thesis are twofold. First, the most correlated defaults are often found among small nearby emerging market economies. This finding supports earlier research by Arellano and Bai (2013) and Arellano, Bai, and Lizarazo (2017) of strategic interaction between defaulting economies. In contrast, the results are hard to couple between economies in Africa and Latin America. Second, I found that the Gompertz (1825) distribution is able to capture between 94–96% (R-squared) of total variation in observed defaults during previous periods of systemic debt crisis. In contrast, the corresponding value for the Gaussian distribution was between 78–91%. This empirical finding indicates that the distributions of past periods of systemic crisis have a tendency to skew and spread out compared to a normal distribution, and thus the assumption for normality can be relaxed. This research adds to earlier research by showing that the four above mentioned empirical distributions vary by their statistical properties. The finding suggests that periods of systemic debt crisis are characterized either by their moderate or fast growth in the total number of sovereign defaults. Consequently, during a risk analysis they should be kept separate because their statistical qualities are not identical. In other words, their distributions differ by their shape and dispersion. The periods characterized by their fast growth (on average 30% p.a.) have a 1% probability for reaching a state where more than a fifth of all economies are in a simultaneous default. The corresponding value for periods characterized by their moderate growth (on average 10% p.a.) is more than half. These results allow practitioners to estimate the expected loss due to the risk of a systemic crisis. In addition, the results show that reducing over-investment in correlated loans and consequent excess correlation of risks in a sovereign debt portfolio can decreases the portfolio’s overall risk.
Thesis advisor
Torstila, Sami
sovereign default, value at risk, risk modelling, treasury bonds
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