# 1 i 12 1 r 12 1 6710 1 4305 09775 14 the forward rate

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=1 + i1,21 + r1,2=1 + 6.710%1 + 4.305%= 0.97751.4 The forward rate of government bonds starting at period 3 and ending at period 4: i3,4=(1 + i0,4)4(1 + i0,3)3− 1 =(1 + 4.2%)4(1 + 3.5%)3− 1 = 6.329%The forward rate of corporate bonds starting at period 1 and ending at period 4: r3,4=(1 + r0,4)4(1 + r0,3)3− 1 =(1 + 5.95%)4(1 + 5.50%)3= 7.312%The marginal probability of repayment at period 4: p3,4=1 + i1,21 + r1,2=1 + 6.239%1 + 7.312%= 0.9908(2)
The cumulative probability of default: pcum= 1 − p0,1× p1,2× p2,3× p3,4= 6.44%(3) If the bank’s hurdle rate is larger than 6.44%, then you will approve the loan. Otherwise, you will not grant this loan. E.g., suppose the bank will approve this type of loans only if the default rate of a borrower is lower than 5%. Company ABC will default at maturity with a probability of 6.44%, higher than the hurdle rate of the bank. Therefore, the bank would not approve this loan application.
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