constitute a default event. Below is a list of the auctions that have been held since 2005. Pricing and valuation There are two competing theories usually advanced for the pricing of credit default swaps. The first, referred to herein as the 'probability model', takes the present value of a series of cashflows weighted by their probability of non-default. This method suggests that credit default swaps should trade at a considerably lower spread than corporate bonds. The second model, proposed by Darrell Duffie, but also by John Hull and Alan White, uses a no-arbitrage approach. Probability model Under the probability model, a credit default swap is priced using a model that takes four inputs; this is similar to the rNPV (risk-adjusted NPV) model used in drug development: the "issue premium", the recovery rate (percentage of notional repaid in event of default), the "credit curve" for the reference entity and the "LIBOR curve". 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 with four quarterly premium payments occurring at times , , , and . If the nominal for the CDS is and the issue premium is then the size of the quarterly premium payments is . 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: either it does not have any default at all, so the four premium payments are made and the contract survives until the maturity date, or a default occurs on the first, second, third or fourth payment date. To price the CDS we now need to assign probabilities to the five possible outcomes, then calculate the present value of the payoff for each outcome. The present value of the CDS is then simply the present value of the five payoffs multiplied by their probability of occurring. This is illustrated in the following tree diagram where at each payment date either the contract has a default event, in which case it ends with a payment of shown in red, where is the recovery rate, or it