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Price a 3-year, 3
Price a 3-year, 3.8% annual coupon, $1000 par bond putable at par in year 1 and year 2, using the following calibrated interest rate model.
Assume annual compounding. Round your answer to 2 decimal places.
|
t = 0 |
t = 1 |
t = 2 |
|
r_2,HH = 5% |
||
|
r_1,H = 3.7% |
||
|
r_0 = 1.5% |
r_2,HL = 3.2% |
|
|
r_1,L = 2.9% |
||
|
r_2,LL = 2.2% |
Expert Solution
| Face value | 1000 |
| Coupon rate | 3% |
| Componding period | 1 |
| Coupon int | 30 |
| Fv + int | 1030 |
| High | |||||
| High | r= | 0.05 | fuu | ||
| r=0.037 | Low | ||||
| S0= | r= | 0.032 | fud | ||
| r=1.5% or 0.015 | Low | ||||
| r=0.029 | Low | ||||
| r= | 0.022 | fdd | |||
| T = 0 | T = 1 | T=2 |
| 3% annual coupon of $1000 par value | ||||||
| So , maturity value = 1000 + (3% *1000) = 1030 | ||||||
| Value at T=2 | = | Maturity value at t=3 discounted + coupon int | ||||
| fuu | (1038/1.05) + 38 | = | 1026.571 | |||
| fud | (1038/1.032) + 38 | = | 1043.814 | |||
| fdd | (1038/1.022) + 38 | = | 1053.656 | |||
| Value at T=1 | = | Maturity value at Average of t=2 discounted + coupon int | ||||
| fu | = | 0.5*(1026.571/1.037)+ 38 + 0.5* (1043.814/1.037)+38 | = | 1074.2569 | ||
| fd | = | 0.5(1043.814/1.029)+38 + 0.5(1053.656/1.029)+38 | = | 1095.1788 | ||
| Value at T=0 | Maturity value at Average of t=1 discounted + coupon int | |||||
| Value | = | 0.5[(1074.2569/1.015)+(1095.1788/1.015)] | 1068.6875 |
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