suppose that a three-year corporate bond provides a coupon of 7% per year payabl
ID: 2742802 • Letter: S
Question
suppose that a three-year corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (expressed with semiannual compounding). The yields for all maturities on risk-free bond is 4% per annum(expressed with semiannual compounding). Assume that defaults can take place every six months(immediately before a coupon payment) and the recovery rate is 45%. Estimate the default probabilities assuming (a) the unconditional default probabilities are the same on each possible default date (b) the default probabilities conditional on no earlier default are the same on each possible default date.
Explanation / Answer
a)
market price of bond =105.3289
risk free value of bond = 108.2837
=>
345.33Q = 2.9548
=> Q = 1.72% (ans)
b)
63.68Q+61.14Q(1-Q)+58.64Q(1-Q)^2+56.19Q(1-Q)^3+53.79Q(1-Q)^4+51.88Q(1-Q)^5 = 2.9548
=>
Q = 1.94%
time Default probability recovery rate risk free value loss given default discount facotr pv of expected loss 0.5 Q 45 109.97 64.97 0.9802 63.68Q 1 Q 45 108.63 63.63 0.9608 61.14Q 1.5 Q 45 107.27 62.27 0.9418 58.64Q 2 Q 45 105.87 60.97 0.9231 56.19Q 2.5 Q 45 104.45 59.45 0.9048 53.79Q 3 Q 45 103.5 58.5 0.8869 51.88Q 345.33QRelated Questions
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