Discount factor of FRA and SWAP

[lavenderwong]

I would like to ask how to calculate the FRA discount rate and Swap discount rate (3M, 6M, 9M, 1Y…etc).


Given,
FRA 1 x 4 0.123%
FRA 2 x 5 0.124%
FRA 3 x 6 0.144%
FRA 6 x 9 0.186%
Swap 1Y 0.234%
Swap 2Y 0.256%
Swap 3Y 0.322%
Swap 4Y 0.412%

Thank you.

 

[S2000magician]

I don’t recall seeing FRA and swap discount rates (as you’ve described) at Level I. Where did you get these numbers?

 

[lavenderwong]

just question from my classmate…… is it level 2?
anyway, is there any simple equation for FRA and SWAP, i can just find some very complex equation in google….

 

[S2000magician]

lavenderwong wrote:just question from my classmate…… is it level 2?
anyway, is there any simple equation for FRA and SWAP, i can just find some very complex equation in google….

A simple question for … what, exactly, about FRAs and swaps?
Are you asking if there’s a simple formula to calculate the price (i.e., the fixed rate) of an FRA? Yes.
To calculate the price of a plain vanilla interest rate swap? Yes.
Something else? Again, what, exactly?

 

[lavenderwong]

sorry for not telling my question clearly, i know solve it.
the problem i got is that for calculating the 1x4 FRA, i dont know the interest rate of 1M. Now i know getting it by bootstrapping, which refer to other money market instrument.
if then, i can get the discount factor easily by 1/(1+t *r)
thank you.

 

[S2000magician]

lavenderwong wrote:sorry for not telling my question clearly, i know solve it.
the problem i got is that for calculating the 1x4 FRA, i dont know the interest rate of 1M. Now i know getting it by bootstrapping, which refer to other money market instrument.
if then, i can get the discount factor easily by 1/(1+t *r)
thank you.

Yes, the fixed rate on a 1×4 FRA is the 3-month forward rate starting 1 month from today; you can calculate that rate using the 1-month spot rate and the 4-month spot rate.
You do not need to know this (for FRAs) for Level I; it’s a Level II topic.