Scheweser book 4 fixed income, LOS 32F swap rate curve. I am stuck on how to calculate this and its driving me nuts.
Can someone break down the mathematical sequence to solve the swap fixed rate tenor of 2 years and get their answer 3.98%? The answer is #2 below, but I have no idea how to get solve for it.
Problem starts:
Example: Swap rate curve
Given the following Libor spot rate curve, compute the swap fixed rate for a tenor of 1, 2 and 3 years (i.e., compute the swap rate curve).
you need to first calculate the implied forward rate given the spot rates
let itsbe the spot rate of interest for t years,
it1,t2f be the implied forward rate of interest from years t1 to t2.
it1,t2f = (1+ it2)t2/ (1 + it1)t1 - 1
(a proper financial math book explains in detail how to get to this formula, which is fundamental in finance. if scheweser book doesnt show this, maybe you deserve a refund). it should also be noted that this formula is only applicable for single periods. multi-period implied forward rate is slightly different)
the implied forward rate for year 0 to 1 is just the spot rate, so i1f = i1s = .03
the implied forward rate for year 1 to 2 is:
i2f = (1.042 / 1.031) - 1 = .050097087
the swap rate is calculated as follows:
sum from t = 1 to n of [i<sub>t1,t2</sub><sup>f </sup>x (1 + i <sub>t </sub><sup>s</sup>) <sup>-t</sup>] / [sum from t = 1 to n of ( 1+ its )-t]
Whatever you do to one side of an equation, ya hafta do to the other!!! have a look at where you multiplied the left hand side by 1.042 and later by 1.03.
Here, for example, you forgot to multiply SFR2/1.03 by 1.042. If you multiply one term by something, you have to multiply every other term by that same something.
Hey thanks for this, and for the foresight to know I have no idea what @breadmaker meant when he said I have to do it to the other side of the equation lol. I now feel like I’ve been doing math wrong for my entire life lolol.