We study computational problems in financial networks of banks connected by debt contracts and credit default swaps (CDSs). A main problem is to determine clearing payments, for instance right after some banks have been exposed to a financial shock. Previous works have shown the \(\varepsilon \) -approximate version of the problem to be \(\textrm{PPAD}\) -complete and the exact problem \(\textrm{FIXP}\) -complete. We show that \(\textrm{PPAD}\) -hardness hold when \(\varepsilon \approx 0.101\) , improving the previously best bound significantly. Due to the fact that the clearing problem typically does not have a unique solution, or that it may not have a solution at all in the presence of default costs, several natural decision problems are also of great interest. We show two such problems to be \(\exists \mathbb {R}\) -complete, complementing previous \(\textrm{NP}\) -hardness results for the approximate setting.