P2.T6.211. Spread-based default probability (PD)
211.1. The risk-free rate is 2.00% and a corporate bond has a yield of 3.50% per annum. It is estimated that the contribution to the spread by all non-credit factors is 40 basis points; e.g., liquidity risk. The recovery rate estimate is 75.0%. What is an approximation (emphasis on "approximation") for the implied default probability?
211.2. The risk-neutral default probability of a one-year corporate BB-rated bond is 5.0% with an estimated loss given default (LGD) of 65.0% while the risk-free rate is 2.0%. If we assume an annual compound frequency, which is nearest to the yield of the corporate bond?
211.3. The following three corporate bonds trade
- Bond A has a price of $97.00, pays no coupon, estimated loss given default (LGD) of 50.0%, and matures in one year
- Bond B has a price of $95.00, a coupon rate of 1.0% (payable semi-annually), estimated LGD of 45.0%, and matures in 1.5 years
- Bond C has price of $96.00, a coupon rate of 2.0% (payable semi-annually), estimated LGD of 40.0%, and matures in 2.0 years
The risk-free rate curve includes: 1.0% at one year; 1.5% at 1.5 years; and 2.0% at two years. If the only contribution to spreads is credit risk (unrealistically, non-credit factors do not contribute to the spread), which bond has the highest market-implied probability of default?
- Bond A
- Bond B
- Bond C
- Cannot determine