AuthorTopic: Credit Risk - market-implied risk-neutral probability of default
Siuva
@2014-11-19 20:45:31
Anyone can tell me how's come of calculation [99 = 104/(1 + y*/200)]?

Question:
Suppose XYZ Corp. has two bonds paying semiannually according to the following table:
Remaining Coupon T-BillRate
Maturity (sa30/360) Price (BankDiscount)
6 months 8.0% 899 5.5%
1 year 9.0% 100 6.0%
The recovery rate for each in the event of default is 50%. For simplicity, assume that each bond will default only at the end of a coupon period. The market-implied risk-neutral probability of default for XYZ Corp. is
a. Greater in the first six-month period than in the second
b. Equal between the two coupon periods
c. Greater in the second six-month period than in the first
d. Cannot be determined from the information provided
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Ans:
a) First, we compute the current yield on the six-month bond, which is selling at a
discount.We solve for y* such that 99 = 104/(1 + y*/200) and find y* = 10.10%.
Thus, the yield spread for the first bond is 10.1 - 5.5 = 4.6%. The second bond
is at par, so the yield is y* = 9%. The spread for the second bond is 9 - 6 = 3%.
The default rate for the first period must be greater. The recover is the same for the two periods, so it does not matter for this problem.

### CFA Discussion Topic: Credit Risk - market-implied risk-neutral probability of default 