Dependency of Real Estate and International Financial Markets – A GARCH-Copula Approach to Model Extreme Market Risk

The behaviour of single investment positions such as securitized real estate, stocks and bonds as well as the dependency between them are central topics in financial literature. Science as well as praxis are constantly seeking for improvements to model risk and returns of financial assets. With regard to the isolated behaviour of positions such as securitized real estate, the asset class shows characteristics, which cause Gaussian assumptions to fail. These include non-normality as well as serial correlation of return distributions. Thus, the extreme value theorem-driven GARCH modelling for volatility patterns is a feasible alternative to model single asset behaviour and its associated risk. Additionally to the isolated behaviour of single assets, the joint behaviour of securitized real estate and other asset classes has widely been discussed. With regard to these dependency features, challenging characteristics such as fat tail exposure, volatility clustering and non-linearity should be highlighted. Thus, the dependency modelling needs more flexible concepts, which allow for upper and lower tail dependency between the return distributions.The paper will solve the above-named challenges by applying the so-called GARCH-EVT-Copula approach. Therefore, financial time series of securitized real estate as well as other asset classes will be individually modelled by classic GARCH models as well as its asymmetric peers including EGARCH, TGARCH, and PGARCH. By doing so, a the iid residuals will be extracted as the proxy for extreme market risk, since they represent the modelling error for each series. Subsequently the joint behaviour of the residuals is modelled by copulas to allow for extreme joint behaviour in the tail region of the distribution. We will then estimate the bivariate copula parameters to assess which kind of copula is the best-fitting type including different dependency structures such as archimedian, elliptical and especially asymmetric copulas. The fit will be assessed based on LL, AIC and BIC citeria. The named fit-parameters for each bivariate copula will reveal the characteristics of extreme market risk, represented by potentially asymmetric lower tail dependent copulas, to illustrate potentially extreme market risk for the joint behaviour.