The 1-year and 2-year CDS spreads on a given reference entity are 100 and 120 basis points, respectively. The risk-free rate is 3% with continuous compounding for all maturities, the recovery rate is 35% and the payments are quarterly. If a default does occur, it is assumed to occur at the mid-point of a quarter. The hazard rates for the first 2 years that are consistent with the 1-year and 2-year CDS spreads are 1.53% and 2.16%, respectively.

1. Suppose the hazard rate for year 3 is 2.25%. Based on this hazard rate together with the hazard rates for the first 2 years, compute the 3-year CDS spread.

1. If the observed 3-year CDS spread is 135 basis points,
2. Using Solver, compute the hazard rate for year 3.
3. What is the probability of default in year 3?