Consider a 5-year bond with a face value of $100 that pays an annual coupon of 6% and is currently rated BBB. The expected recovery rate in case of default is 51.13%. In the table below, you are given the probabilities that in one year (i) the bond issuer maintains its BBB rating, (ii) is upgraded to AAA, AA or A or downgraded to BB, B or CCC and (iii) defaults. Rating Probability (%) AAA AA A BBB BB B CCC Default Consider also the one-year forward yield curve for zero-coupon bonds with different maturities and credit ratings (rates are discretely compounded): Years to Maturity 2 years 4.17% 4.22% 4.32% 4.67% 6.02% 7.02% 15.02% Rating AAA AA A BBB BB B CCC 0.02 0.33 5.95 86.93 5.3 1.17 0.12 0.18 1 year 3.60% 3.65% 3.72% 4.10% 5.55% 6.05% 15.05% 3 years 4.73% 4.78% 4.93% 5.25% 6.78% 8.03% 14.03% 4 years 5.12% 5.17% 5.32% 5.63% 7.27% 8.52% 13.52%
Consider a 5-year bond with a face value of $100 that pays an annual coupon of 6% and is currently rated BBB. The expected recovery rate in case of default is 51.13%. In the table below, you are given the probabilities that in one year (i) the bond issuer maintains its BBB rating, (ii) is upgraded to AAA, AA or A or downgraded to BB, B or CCC and (iii) defaults. Rating Probability (%) AAA AA A BBB BB B CCC Default Consider also the one-year forward yield curve for zero-coupon bonds with different maturities and credit ratings (rates are discretely compounded): Years to Maturity 2 years 4.17% 4.22% 4.32% 4.67% 6.02% 7.02% 15.02% Rating AAA AA A BBB BB B CCC 0.02 0.33 5.95 86.93 5.3 1.17 0.12 0.18 1 year 3.60% 3.65% 3.72% 4.10% 5.55% 6.05% 15.05% 3 years 4.73% 4.78% 4.93% 5.25% 6.78% 8.03% 14.03% 4 years 5.12% 5.17% 5.32% 5.63% 7.27% 8.52% 13.52%
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:a) Compute the volatility of the above bond in one year.
b) Is the volatility a coherent risk measure? Explain.
c) Compute the 1-year Value-at-Risk and Expected Shortfall of the above
bond at a 99% confidence level.
Transcribed Image Text:Consider a 5-year bond with a face value of $100 that pays an annual coupon
of 6% and is currently rated BBB. The expected recovery rate in case of
default is 51.13%. In the table below, you are given the probabilities that in
one year (i) the bond issuer maintains its BBB rating, (ii) is upgraded to AAA,
AA or A or downgraded to BB, B or CCC and (iii) defaults.
Rating
Probability (%)
AAA
0.02
AA
0.33
A
5.95
BBB
86.93
BB
5.3
B
1.17
CCC
0.12
Default
0.18
Consider also the one-year forward yield curve for zero-coupon bonds with
different maturities and credit ratings (rates are discretely compounded):
Years to Maturity
Rating
1 year
2 years
3 years
4 years
3.60%
4.17%
4.73%
5.12%
3.65%
4.22%
4.78%
5.17%
3.72%
4.32%
4.93%
5.32%
4.10%
4.67%
5.25%
5.63%
5.55%
6.02%
6.78%
7.27%
6.05%
7.02%
8.03%
8.52%
15.05%
15.02%
14.03%
13.52%
AAA
AA
A
BBB
BB
B
CCC
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