RDP 2013-12: Central Counterparty Links and Clearing System Exposures Equation

\begin{array}{l} Y_{U} = (σ_{1} + σ_{2}) \frac{N \sqrt{N - 1}}{\sqrt{2 π}} \\ Y_{L} = (σ_{1} + σ_{2}) \frac{N' \sqrt{N - 1}}{\sqrt{2 π}} + (N_{1} + N_{2}) \frac{\sqrt{(N - 1) (σ_{1}^{2} + σ_{2}^{2} + 2 ρ σ_{1} σ_{2})}}{\sqrt{2 π}} \\ + 2 \frac{\sqrt{N' (N_{1} σ_{2}^{2} + N_{2} σ_{1}^{2}) + N_{1} N_{2} (σ_{1}^{2} + σ_{2}^{2} + 2 ρ σ_{1} σ_{2})}}{\sqrt{2 π}} \end{array}