Explanation:
A: 95.1374 (nearest).
The Eurodollar futures contract is based on the 3-month USD LIBOR (quoted on an actual/360 basis). The futures price quote = 100 − (futures 3-month LIBOR in percent). To find this, first derive the implied 3-month forward LIBOR from the given spot rates (continuous compounding, actual/365).
Discount factors:
DF₉ = e^(−0.025 × 0.75) ≈ 0.981425
DF₁₂ = e^(−0.031 × 1) ≈ 0.969476
Growth factor over the 3-month forward period = DF₉ / DF₁₂ ≈ 1.012325.
For Eurodollar LIBOR (actual/360), use τ = 91.25/360 ≈ 0.253472 (standard quarter assumption consistent with actual/365 year).
Forward LIBOR (L) = (1.012325 − 1) / 0.253472 ≈ 0.048626 (4.8626%).
Futures quote = 100 − 4.8626 ≈ 95.1374.
This matches option A exactly. (Options B–D are too high, implying unrealistically low forward rates around 1–3%.) The calculation aligns with standard no-arbitrage forward rate extraction in Hull-style problems, adjusting only for the actual/360 quoting convention of Eurodollar LIBOR.
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Question 721.1. Suppose that the nine-month LIBOR interest rate is 2.50% per annum and the one-year LIBOR interest rate is 3.10% per annum, both expressed per annum with actual/365 and continuous compounding. Which of the following is nearest to the 3-month Eurodollar futures price quote for a contract maturing in nine months? (note: inspired by Hull’s EOC Problem 6.13)
A
95.1374
B
96.9000
C
97.5000
D
98.2693