In this paper we propose a novel methodology for modelling the dynamics of the volatility related to the differential between each country's 10 Years Sovereign Bond Yield and the 10 Years U.S. Sovereign Bond Yield, namely conditional volatility of the spread. We resort to the AR(1)-EGARCH(1,1)/DCC(1,1) specification for monitoring the evolution of this indicator that considers the co-movement between sovereign bond yields, a crucial unstable component during a Sovereign Debt crisis. The analysis has been developed on weekly data in order to take into account asynchronicity issues that arise in international analysis, as well as considering the exchange rate as an exogenous variable. We further simulate, via bootstrapping, the dynamics of this indicator using the current levels of volatilities and correlations as starting conditions, and forecast the dynamics of the conditional volatility of the spread at different horizons ahead and across scenarios. The analysis, developed on a sample of 32 economies, makes allowance to provide a sensitive procedure based on market available information.