A company has issued two- and four year bonds, each of which has a coupon of 5% per annum, payable semi-annually. The yields on these two bonds are 5% and 6% (with continuous compounding). The recovery rate is 40%. The risk free yield is flat at 4.5% with continuous compounding.
The defaults of the corporate bond can take place at the end of the first quarter of each year. The unconditioal risk-neutral default rates per year are Q1 for years 1 and 2, and Q2 for years 3 and 4.
Required: Estimate Q1 and Q2.