Validate Correlation of an ESG: Treasury Yields acrossEconomies

Within an internal model the Economic Scenario Generator (ESG) is an important component. In orderto get a regulatory approval of an internal model it is required that the implemented models (must be) passeda rigorous validation process, see Ceiops [2009].In this paper we focus on the particular problem to judge the contribution of correlations between interestrate risks across countries in the ESG. To that end we apply two strategies: an analytical and a statisticalone. The analytical approach yields necessary conditions in terms of upper and lower bounds for correlationswithin the chosen model. A system of stochastic differential equations is used to describe several economiessimultaneously. In this framework we derive a lower and upper bound of the correlation of the treasury yieldsbetween two economies by solving the associated ordinary differential inequalities...