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A ) During your co - op term at RBC , you are asked to assess the credit risk of an 8 - year corporate

A)
During your co-op term at RBC, you are asked to assess the credit risk of an 8-year
corporate bond that provides a coupon of 4.4% per year payable annually and has a
yield of 6.25%(continuous compounding). The yields for all maturities on risk-free
bonds are 3.85% per year (continuous compounding). Assume that defaults can take
place every 6 months, either in the middle of the year or at the end of the year
immediately before a coupon payment. The recovery rate is 41%. Assuming that the
unconditional default probabilities are the same on each possible default date. What is
the approximate default probability? What is the more accurate default probability?
B)
Repeat question A) by assuming that the 41% recovery rate is applied to the market
value of the risk-free bond as opposed to par. Compare the default probability with
that in A) and explain the difference. Note: in practice, the recovery rate is applied to
the par. Only in this question, we make the special assumption in order to derive
some insights.
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