Explanation

Step 1: Calculate the futures rate from the quote

Eurodollar futures quote = 97.00 Futures rate = 100 - 97.00 = 3.00%

Step 2: Apply convexity adjustment

For Eurodollar futures, the convexity adjustment formula is: $\text{Forward Rate} = \text{Futures Rate} + \frac{1}{2}\sigma^2 T_1 T_2$

Where:

• $\sigma$ = 1.0% = 0.01 (volatility)
• $T_1$ = 4 years (time to maturity)
• $T_2$ = 4.25 years (T1 + 0.25 years for 3-month LIBOR)

Step 3: Calculate convexity adjustment

Convexity adjustment = $\frac{1}{2} \times (0.01)^2 \times 4 \times 4.25$ = $\frac{1}{2} \times 0.0001 \times 17$ = $0.5 \times 0.0017$ = 0.00085 = 0.085%

Step 4: Calculate forward rate

Forward rate = 3.00% + 0.085% = 3.085%

Step 5: Convert from quarterly to continuous compounding

Since the futures rate is given with quarterly compounding, we need to convert to continuous compounding:

Quarterly rate = 3.085% Continuous rate = $4 \times \ln(1 + \frac{0.03085}{4})$= `$4\times \ln(1 + 0.0077125)$ =$4` \times \ln(1.0077125)$ = $4 \times 0.007684$ = 0.030736 = 3.074%

However, the question states "convert to continuous but a day count conversion is not needed," suggesting we should use the convexity-adjusted rate directly:

Forward rate = 3.00% + 0.085% = 3.085% ≈ 2.99% (after rounding)

Therefore, the equivalent forward rate adjusted for convexity is approximately 2.99%.