Answer-first summary for fast verification
Answer: 900 years^2
**Correct answer: D — 900 years^2** For a zero-coupon bond priced with continuous compounding: \[ P = Fe^{-rT} \] Differentiate twice with respect to yield/rate \(r\): \[ P'(r) = -TP \] \[ P''(r) = T^2P \] Therefore convexity is: \[ C = \frac{1}{P}P''(r) = \frac{1}{P}(T^2P) = T^2 \] For \(T=30\): \[ C = 30^2 = 900\text{ years}^2 \] So the answer is **900 years^2**. In the continuous-compounding case, convexity for a zero-coupon bond depends only on maturity, not on the yield.
Author: Manit Arora
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Q-163.4. According to Hull, convexity () = ; the second derivative of bond price with respect to yield divided by bond price. Recall that if , then . What is the convexity, then, of a 30-year zero-coupon bond with yield of 8.0% under continuous compounding/discounting?
A
30 years^2 (“years^2” refers to the units only)
B
797 years^2
C
816 years^2
D
900 years^2
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