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Answer: 3.239%
The futures quote of 96.00 implies a 3-month Eurodollar rate of **4.00%**. To extend the zero curve from 300 days to 390 days, we combine: - the existing **300-day continuous ACT/365 zero rate** of 3.0%, and - the **90-day forward rate** implied by the futures contract. ### Step 1: Discount factor to 300 days \[ P(0,300)=e^{-0.03\cdot 300/365} \] ### Step 2: Forward factor for the next 90 days A 4.00% quarterly-compounded rate over 90 days implies a growth factor of: \[ 1+\frac{0.04}{4}=1.01 \] So: \[ P(0,390)=\frac{P(0,300)}{1.01} \] ### Step 3: Solve for the 390-day continuous zero rate \[ e^{-z_{390}\cdot 390/365}=\frac{e^{-0.03\cdot 300/365}}{1.01} \] Taking logs: \[ z_{390}=\frac{0.03\cdot 300/365+\ln(1.01)}{390/365} \approx 3.239\% \] So the correct answer is **B. 3.239%**.
Author: Manit Arora
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Q-173.1. The 300-day LIBOR zero rate is 3.0% per annum with ACT/365 continuous compounding. The Eurodollar futures quote for a contract maturing in 300 days is 96.00; as usual, the Eurodollar interest rate is expressed with ACT/360 quarterly compounding. What is the 390-day LIBOR zero rate with ACT/365 continuous compounding (i.e., as we are extending the LIBOR zero curve)? Please assume that the convexity adjustment is effectively zero here, due to the short maturities involved; i.e., assume the forward rate is equal to the futures rate.
A
3.006%
B
3.239%
C
3.867%
D
4.035%
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