Market risk calculations in stock- and bond prices: a garch-copula approach

The financial crisis of $2008$-$2009$ has led to more strict regulatory supervisory on banks and insurance companies, focusing on better (market) risk models. The linear correlation models did not foresee the extreme losses in asset values, because they were not able to forecast high volatile markets in which the dependence between financial assets seemed to increase. Research on copula theory, a tool to model more advanced dependence structures, predominately analyses the effect of the copula on highly dependent stock indexes, often using one underlying simulation model. This study compares two slightly dependent equity and bond prices for four different combinations of univariate simulation models, including Black-Scholes, Hull-White, GARCH and different residual models, three different copula models (Gaussian, Student $t$ and flipped Gumbel) and two calibration methods. The goal is to measure the effect of different copula dependence models in economic scenario generators in combination with different simulation models and compare results in terms of accuracy, stability, resilience and complexity. The main result is that due to the little dependence the impact of the copula model is limited and dependence in the copulas is small compared to the estimations based on stressed markets. Hence, for these low dependent portfolios the copulas do not have much added value. Remarkable is that the dependence implied by the copula can strongly depend on the underlying model. The estimated dependence parameters of the copulas are lower for models using a GARCH volatility model. This can be explained by the non independent identically distributed residuals in the model without GARCH, i.e. the high volatile market periods lead to volatility clustering in the residuals. If this volatility clustering is not captured by the model, it can lead to amplification of the dependence due to misfitting of the univariate simulation models. The differences in risk estimations are mainly caused by the choice of simulation models. The GARCH volatility model leads to an increase in the calculated market risk at a horizon of one year. The choice of residual model has large impact on the risk calculations in one day and (depending on the strength of the dependence) can have both negative and positive impact on the risk calculations in one year and the choice of simulation models should therefore be chosen with care.Electrical Engineering, Mathematics and Computer ScienceMathematic