A company has issued 3- and 5-year bonds with a coupon of 4% per annum payable annually. The yields on the bonds (expressed with continuous compounding) are 4.5% and 4.75%, respectively. Risk-free rates are 3.5% with continuous compounding for all maturities.
The recovery rate is 40%. Defaults can take place halfway through each year. The risk-neutral default rates per year are Q1 for years 1 to 3 and Q2 for years 4 and 5. Estimate Q1 and Q2.