This paper presents a theoretical and numerical framework where the Gamma-Hedging of a Multi-Name Synthetic Collateralized Debt Obligation (SCDO) is defined. Gamma is numerically calculated in order to compute the Profits and Losses shape of each tranche. A further analysis which has been developed is the understanding and quantification of the impact of a joint shift of both Credit Default Swap (CDS) spread and default correlation under different recovery rates. The model used for the purpose of this work is the One-Factor-Copula and the main assumption considered is a finite and homogeneous portfolio.