Answer-first summary for fast verification
Answer: d) 6.0270%
For a par bond, the price is 1.0, and Hull's formula is: \[ 1 = A\cdot \frac{c}{m} + d \] where: - \(A\) is the sum of discount factors for each coupon date, - \(d\) is the discount factor at maturity, - \(m = 2\) because coupons are paid semi-annually. Given: - \(A = 3.75310\) - \(d = 0.8869\) Solve for \(c\): \[ c = m\cdot \frac{1-d}{A} = 2\cdot \frac{1-0.8869}{3.75310} \] \[ c = 2\cdot \frac{0.1131}{3.75310} \approx 0.06024 = 6.024\% \] The nearest choice is **d) 6.0270%**.
Author: Manit Arora
Ultimate access to all questions.
Q-715.1. Consider the following continuously compounded zero (spot) rate curve and their associated discount factors; e.g., df(1.5) = exp(-0.0540*1.5) = 0.9222.
| Maturity (yrs) | Zero Rates (Continuously Compounded) | Discount Factors (df) |
|---|---|---|
| 0.5 | 3.00% | 0.9851 |
| 1.0 | 4.20% | 0.9589 |
| 1.5 | 5.40% | 0.9222 |
| 2.0 | 6.00% | 0.8869 |
| Sum: | 3.75310 |
Zero (spot) rate curve
[Image blocked: Zero (spot) rate curve]
What is nearest to the per annum par yield, if we follow Hull and express the par yield with continuous compounding while the coupon is paid semi-annually? Hint: per Hull, the par yield, denoted by (c), must satisfy $1.0 = A \cdot c/m + 1.0 \cdot d, where (d) is the present value of \`1.0` received at the maturity of the bond, (A) is the value of an annuity that pays one dollar on each coupon payment date, and (m) is the number of coupon payments per year.
A
a) 3.7420%
B
b) 4.0330%
C
c) 5.1890%
D
d) 6.0270%
No comments yet.