1. Measuring Default Risk from Market Price
Multiple Periods
Assume that the bond has only one payment of $100 in T periods: P
Default: f*100
No Default: 100

2. Cumulative Default Rate
Measuring Default Risk from Market Price
Multiple Periods :
Survival Rate
Cumulative Default Rate
Multiplying by (-1) and adding 1:

3. Measuring Default Risk from Market Price
Which can be rewritten as :
CDRT is the Cumulative Default Rate at year T.

4. Measuring Default Risk from Market Price
Assuming that the yield also reflects risk premium:

5. Measuring Default Risk from Market Price
Numerical Example
IBM 10-year zero coupon bond is rated A. The bond is traded at 7% YTM and Treasury 10-year zero coupon bond traded at 6% YTM. The recovery rate is 45%.
What is the cumulative default rate for 10 years?
What is the average marginal default rate?
The Cumulative Default Rate (CDR) for 10 years is:

6. Measuring Default Risk from Market Price

7. Measuring Default Risk from Market Price
According to S&P data the 10-year CDR for A rated bond is only 3.5%.
The deference induced by the fact that a large part of the credit spread reflects a risk premium.
For instance, assume that 0.7% out of the credit spread reflects a risk premium.
In this case the 10-year CDR is:

8. Measuring Default Risk from Equity Prices
The credit spread approach is only useful when there is a good bond market data.
In practice, there are many countries that do not have a developed bond market.
In addition, the firm may do not have publicly traded bond.
In this case we can use the firm’s stock price in order to estimate the credit risk parameters