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5#
发表于 2014-4-23 18:33
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1. Credit Risk Measures
EX1: Calculation of “Present Value of Expected Loss”:
Consider a 1,000 par value, 3-year, 6% semiannual coupon bond. Risk-free rates and
credit spreads for the next 3 years are given in the table below:
Note: All rates are continuously compounded.
Calculate the present value of expected loss for
1. The payment due in 2 years;
2. The bond
Time (yrs) Risk-Free Rate Credit Spread
0.5 0.11% 0.03%
1.0 0.16% 0.07%
1.5 0.21% 0.08%
2.0 0.22% 0.09%
2.5 0.27% 0.09%
3.0 0.31% 0.10%
Present Value of Expected Loss =Value of an otherwise identical risk-free bond – Value of a credit-risky bond
Time Cash Flow Risk-Free Rate Credit Spread Total Yield PV (Risk-Free) PV (Risky) Difference
0.5 30 0.11% 0.03% 0.14% $29.98 $29.96 $0.02
1.0 30 0.16% 0.07% 0.23% $29.95 $29.88 $0.07
1.5 30 0.21% 0.08% 0.29% $29.91 $29.78 $0.13
2.0 30 0.22% 0.09% 0.31% $29.87 $29.68 $0.18
2.5 30 0.27% 0.09% 0.36% $29.80 $29.53 $0.27
3.0 1030 0.31% 0.10% 0.41% $1,020.47 $1,007.99 $12.47
Total: $1,169.97 $1,156.83
PV
n
=CF
n
×e –(yield×n)
PV (risk-free)
1st coupon
= 30 ×
e (-0.0011)(0.5) =$29.98
2. PV of Expected Loss = PV(Risk-free) – PV(Risky)
=$1,169.97-$1,156.83=$13.15
PV of expected loss is the highest price an investor
would be willing to pay to an insurer to bear the credit
risk of the investment.
1. PV of Expected Loss for pmt due in 2 years
= PV(Risk-free)
pmt2
– PV(Risky)
pmt2
=$29.87-$29.68
=$0.18 |
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