Before revision:  Conditions for absence of arbitrage and valuation formulas for tranches of CDOs are given .
After revision:  Conditions for absence of arbitrage , explicit examples, an affine setup which includes contagion and pricing formulas for STCDOs and options on STCDOs. A calibration to iTraxx data with an extended Kalman filter shows an excellent fit over the full observation period. The calibration is done on a set of CDO tranche spreads ranging across six tranches and three maturities .