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Suppose that a three-day corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (express with semiannual compounding)

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Suppose that a three-day corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (express with semiannual compounding). The yields for all maturities on risk-free bonds 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 and (b) the default probabilities conditional on no earlier default are the same on each possible default date.