Estimating a 1x4 FRA from a LIBOR Curve

# Calculating FRA rates


# Calculating FRA rates












Let's assume I constructed usd libor 3M curve setting 1M rate=3M rate (so the curve is flat between 1M-3M). Will 1x4 FRA rates be good if calculated from such curve?

## Answer by Dom (score 1)

https://quant.stackexchange.com/a/29478

The 1x4 FRA rate is given by

$F(1,4) = \frac{12}{3} \left(\frac{(1+ 4/12 \times L(4))}{(1+ 1/12 \times L(1))}-1 \right)$

where $L(T)$ is the $T$-month Libor rate seen today.

Clearly $F(1,4)$ depends on the 1M and 4M LIBOR rates.

So if the market 1M rate $L(1)$ is below the market 3M rate $L(3)$ you will be understating the true FRA rate if you set $L(1)=L(3)$

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/29483

The 1x4 FRA rate is where you can lock in 3 mo libor , 1 mo from now. To construct this rate , you must build a 3 mo libor curve. The first point in this curve is 0x3 libor , which is spot 3 mo libor. The next point on this curve is the next Eurodollar futures contract. These expire every month on the third Wednesday. Then you have to interpolate between the points you can observe. Today's value of 1 month libor is completely irrelevant to this calculation.

## Answer by Ami44 (score 0)

https://quant.stackexchange.com/a/29558

To value a 1x4 FRA you need the forward rate f(1,4) from a 3 Month yield curve. For that you need the discount factors at 1 month and 4 months. The 1 month discount factor can be extracted from the 1 month libor rate. But for the 4 month discount you can not use the 4 month libor. You can use swaps with 4 month left to maturity and payment frequency 3 month but these are not very liquid. Also often FRA quotes are used for these timebuckets below 1 year. of course you can also just interpolate between a 3 month zerorate from libor and a 1 year zerorate from swaps. That would be the most simple solution. Above 1 year swap rates are normally much more reliable than below.