XYZ Inc. whose stock is currently valued at $125/share with an implied volatility of 40% has debt of $80/share.
a. Assuming a global recovery rate of 50% and a standard deviation of recovery rate of 30%, estimate its 4 and 5 year default probability.
b. Estimate the unconditional and conditional default probability in year 5.
c. Based on the market CDS quotes, the implied 5 year default probability is 5%. Determine the correct Global Recovery Rate that would make XYZ 5 year default probability equal to 5% (Keep the standard deviation of recovery rate the same)