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Ok, thank you for that clarification.
So, maybe it would be a better way to let my term structures reference date to the settlement date (09-04-2015) and to use this DiscountingSwapEngine constructor (where I set includeSettlementDate to true):
IPricingEngine assetSwapEngine = new DiscountingSwapEngine( Program.currentYieldCurves.discountingTermStructure, true);
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