If default events never occurred the price of a CDS would simply be the sum of the discounted premium payments. So CDS pricing models have to take into account the possibility of a default occurring some time between the effective date and maturity date of the CDS contract. For the purpose of explanation we can imagine the case of a one-year CDS with effective date formula_1 with four quarterly premium payments occurring at times formula_2, formula_3, formula_4, and formula_5. If the nominal for the CDS is formula_6 and the issue premium is formula_7 then the size of the quarterly premium payments is formula_8. If we assume for simplicity that defaults can only occur on one of the payment dates then there are five ways the contract could end: