Copula modeling analysis on multi-dimensional portfolios with backtesting
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In recent years, risk management has become one of the most crucial areas in the financial industry. The main interest of financial researchers is how to measure risk effectively and reliably. For this purpose, Value-at Risk (VaR) has been designed to make such measurements. However, VaR measurements are not usually accurate, especially for multi-dimensional portfolios. Because the dependency structures among each asset in a given portfolio cause the measuring problem, we need to find valid ways to overcome or avoid potential obstacles. In this thesis, Copula models are built step by step to predict VaR(α) of multi-dimensional portfolios. Additionally, our common Copula models are applied in real cases in order to see their universality, namely, to see how large the portfolio’s dimensions can be before the model fails, and to see which models predict VaR(α)s more accurately. We use backtesting, a criterion with two hypothesis test called Unconditional Coverage Test and Conditional Coverage Test, for additional verification.