Help!
I can’t seem to solve and get the swap fixed rate Spot LIBOR rate Year1 - 3% Year2 - 4% Year3 - 5% Spot fixed rate for a tenor of 2 year = 3.98% <<<< Equation [SFR/ 1.03] + [SFR/ (1.042)] + [1/(1.042)] = 1 My steps: #1) 1/1.042 = .92456 #2) 1-.92456 = .07544 #3) [SFR/ 1.03] + [SFR/ (1.042)] = .07544 #4) .07544 * 1.03 = .07766 #5) .7766 * (1.042) = .08400 #6) .084 = SFR + SFR #7) .042 = SFR IS this correct? Help please
Are you trying to find the 2 year swap fixed rate? You’re calling it the spot fixed rate?
Discount for Year1 = 1/1.03 = .970873
Discount for Year2 = 1/(1 + .04x2) = .9259259
Sum of Year1 and Year2 = 1.8967989
SFR for 2 year swap, annual pay = (1- 9259259) / 1.8967989 = 3.90%
Yes I am. Darn, I think I had a brain freeze moment. Updated*
I don’t understand your formula. Why are you multiplying the .04 by 2, and how did you get the final step where
(1- 9259259) / 1.8967989 = 3.90%
Do you have a formula that you follow?
Yes I use an easier formula.
First, you find all the discount rates. To find the discount rate for year2, you multiple the annual rate by 2 and then add 1. To find the discount rate for year 3, you multiple by 3 and then add 1. If you were to find discount rate for a 90 day libor, you would divide by 4, Or you can do (1 + R*90/360)… (And obviously take the reciprocal.
After you find all the discount rates, add them up… that becomes your denominator for the SFR. THe numberator is just 1-final_discount_rate. Here, since year2 is the final one, its 1 - Discount Rate of year 2.
The rates are LIBOR. They’re nominal rates, not effective rates. They don’t compound.
SFR = (1 − zn) / Σ_zi_
Okay, got it. Can you also help me with this. What if they just give you the price? Schweser uses this but I don’t understand it completely… SFR3 (P1 + P2 + P3) + P3 = 1
Plug in what we just did…
SFR2 = 0.039
Σ_zi =_ P1 + P2 = 1.8967
P2 = .92592
0.039 (1.8967) + .92592 = 1
It’s all algebra.
SFR = (1 − zn) / Σ_zi_
==> SFR x Σ_zi_ = (1 − zn)
==> SFR x Σ_zi_ + zn= 1
okay, thank you very much. I will revisit this again tomorrow. I think my brain is fried.
@125mph I’m trying to follow your instructions to calculate the SFR payment for a tenor of 3 years (for the original post/ problem). Numerator:1 -[1/ (1+ .05*3)] = .130435 Denominator = [1/1.03] + [1/1 +.04*2] + [1/ 1 + .05*3] Book says its 4.93% but I’m getting 4.715%
I get 4.7150%.
If the spot rates are effective rates (not nominal rates), then I get 4.9347%.
You’re quite welcome.