Two things: 1) The eurodollar implied futures rates need to be convexity-adjusted before they can be used as forward rates (futures rate = forward rate + convexity bias). 2) Discounting should be done using the OIS discount curve, not the LIBOR curve.

More specifically (and ignoring market conventions such as day count), let's say you're pricing a 1-year swap (6m fixed vs 3m floating) and let's assume that all the Eurodollar futures are perfectly aligned with the floating leg (i.e., there's no stub period and start & end dates are matched). Then step 1 is to compute the implied forward rates from the Eurodollar futures, which are $100 - \text{ED prices} - \text{convexity adjustments}$, where the convexity adjustments can be obtained using simple models or from dealers. Then the par swap rate is solved from $$ \frac{c}{2} \cdot d(0.5) + \frac{c}{2} \cdot d(1.0) = F_{0,0.25}\cdot 0.25 \cdot d(0.25) + F_{0.25,0.5}\cdot 0.25 \cdot d(0.5) + F_{0.5,0.75}\cdot 0.25 \cdot d(0.5) + F_{0.75,1}\cdot 0.25 \cdot d(1), $$

where $c$ is the par coupon rate you're solving for, $F_{t_1,t_2}$'s are the forward rates between $t_1$ and $t_2$, and $d(t)$ is the OIS discount factor from time $t$ back to the settlement date.

Two things: 1) The eurodollar implied futures rates need to be convexity-adjusted before they can be used as forward rates (futures rate = forward rate + convexity bias). 2) Discounting should be done using the OIS discount curve, not the LIBOR curve.

More specifically (and ignoring market conventions such as day count), let's say you're pricing a 1-year swap (6m fixed vs 3m floating) and let's assume that all the Eurodollar futures are perfectly aligned with the floating leg (i.e., there's no stub period and start & end dates are matched). Then step 1 is to compute the implied forward rates from the Eurodollar futures, which are $100 - \text{ED prices} - \text{convexity adjustments}$, where the convexity adjustments can be obtained using simple models or from dealers. Then the par swap rate is solved from $$ \frac{c}{2} \cdot d(0.5) + \frac{c}{2} \cdot d(1.0) = F_{0,0.25}\cdot 0.25 \cdot d(0.25) + F_{0.25,0.5}\cdot 0.25 \cdot d(0.5) + F_{0.5,0.75}\cdot 0.25 \cdot d(0.75) + F_{0.75,1}\cdot 0.25 \cdot d(1), $$

where $c$ is the par coupon rate you're solving for, $F_{t_1,t_2}$'s are the forward rates between $t_1$ and $t_2$, and $d(t)$ is the OIS discount factor from time $t$ back to the settlement date.

Two things: 1) The eurodollar futures rates need to be convexity-adjusted before they can be used as forward rates (futures rate = forward rate + convexity bias). 2) Discounting should be done using the OIS discount curve, not the LIBOR curve.

More specifically (and ignoring market conventions such as specific day counts), let's say you're pricing a 1-year swap rate (6m fixed vs 3m floating) and let's assume that all the Eurodollar futures are perfectly aligned with the floating leg (i.e., there's no stub period). Then step 1 is to compute the implied forward rates from the Eurodollar futures, which are $100 - \text{ED prices} - \text{convexity adjustments}$, where the convexity adjustments can be obtained using simple models or from dealers. Then the par swap rate is simply solved from $$ \frac{c}{2} \cdot d(0.5) + \frac{c}{2} \cdot d(1.0) = F_1\cdot 0.25 \cdot d(0.25) + F_2\cdot 0.25 \cdot d(0.5) + F_3\cdot 0.25 \cdot d(0.5) + F_4\cdot 0.25 \cdot d(1), $$

where $c$ is the par coupon rate you're solving for, $F_i$'s are the forward rates, and $d(t)$ is the OIS discount factor from time $t$ back to the settlement date.

Two things: 1) The eurodollar implied futures rates need to be convexity-adjusted before they can be used as forward rates (futures rate = forward rate + convexity bias). 2) Discounting should be done using the OIS discount curve, not the LIBOR curve.

More specifically (and ignoring market conventions such as day count), let's say you're pricing a 1-year swap (6m fixed vs 3m floating) and let's assume that all the Eurodollar futures are perfectly aligned with the floating leg (i.e., there's no stub period and start & end dates are matched). Then step 1 is to compute the implied forward rates from the Eurodollar futures, which are $100 - \text{ED prices} - \text{convexity adjustments}$, where the convexity adjustments can be obtained using simple models or from dealers. Then the par swap rate is solved from $$ \frac{c}{2} \cdot d(0.5) + \frac{c}{2} \cdot d(1.0) = F_{0,0.25}\cdot 0.25 \cdot d(0.25) + F_{0.25,0.5}\cdot 0.25 \cdot d(0.5) + F_{0.5,0.75}\cdot 0.25 \cdot d(0.5) + F_{0.75,1}\cdot 0.25 \cdot d(1), $$

where $c$ is the par coupon rate you're solving for, $F_{t_1,t_2}$'s are the forward rates between $t_1$ and $t_2$, and $d(t)$ is the OIS discount factor from time $t$ back to the settlement date.