In order to value new CDS deals, we usually infer the default probability and the

recovery rate from traded CDS, just as we would estimate the volatility from existing

options in order to use the Black-Scholes formula when valuing options. Suppose we

have two CDS contracts on the same company's bonds. One is a 3-year CDS on a

junior subordinated bond with a spread of 390.25bp and the other is a 5-year CDS on

a senior subordinated bond with a spread of 358.78pb. Both contracts have a value of

zero right now. Suppose the LIBOR rate is 3.6%, defaults occur in the middle of the

year, and payments are made annually, in arrears. Historically, the recovery rate for

senior subordinated bonds is 5% higher than the recovery rate for junior subordinated

bonds (e.g., if the former is 35%, then the latter is 30%). Further suppose that all

bonds are in default if default occurs. Please estimate the recovery rate and the default

probability during a year conditional on no early defaults