Hi everyone,I have a question regarding Fujji, Shimada and Takahashi's paper "A note on Construction of multiple swap curves with and without collateral". Specifically, the cross currency swap with US libor as the discounting rate without collateral, [$]N_t^Y\{-P_{t,T_0}+\sum_{n=1}^{N}\delta_n(E_t[L(T_{n-1},T_n)]+b_{t,N})P_{t,T_n}+P_{t,T_N}\}= \frac{N_t^\$}{S_t}\{-P_{t,T_0}^\$+\sum_{n=1}^{N}\delta_n^\$E_t^\$[L^\$(T_{n-1},T_n)]P_{t,T_n}^\$+P_{t,T_N}^\$\}[$], since the right hand side of the equation is zero, we should have the following relationship for the euro leg: [$]\sum_{n=1}^{N}(\Delta_nC_N+\delta_nb_N)P_{t,T_n}=P_{t,T_0}-P_{t,T_N}[$]. By setting N=1,....,N, we're suppose to determine the adjusted euro discount curve, however, how do we determine the discount factor to the effective starting date T_0, [$]P(t, T_0)[$]? Can any one shed some light on this?