# Swaps

I apologize for trolling, however, some answers are harder to find and swaps are a bit difficult for me to understand. I am having trouble with the following question:

Consider an interest rate swap with residual maturity of (exactly) 4 years and the notional principal of € 100 million. You pay 8% fixed annual rate in semiannual payments and receive semiannual cash flows based on the 6-month Euribor rate. Next payment is based on 6m Euribor from the previous reset date, which was 9% annually. The current term structure of zero-coupon rates is flat at 8%. (a) What is the value of the swap? (b) What should be the swap rate such that the price of this swap is zero? Thanks

(a) What is the value of the swap?

The value of a swap is simply the difference of the PV of the fixed-rate leg payments and the PV of the variable-rate leg payments. Depending on whether you are on the receiver or payer side the value is positive or negative (zero at inception or in the very rare case of a totally flat yield curve)

PV of fixed-rate leg minus variable-rate leg on a notional of €100:

YR0.5 = €4.0 - 4.5 =-0.5 YR1.0 = €4.0 - 4.0 = 0.0 YR1.5 = €4.0 - 4.0 = 0.0 YR2.0 = €4.0 - 4.0 = 0.0 YR2.5 = €4.0 - 4.0 = 0.0 YR3.0 = €4.0 - 4.0 = 0.0 YR3.5 = €4.0 - 4.0 = 0.0 YR4.0 = €4.0 - 4.0 = 0.0 You see that given the term structure the PV is zero except for the first payment after 6 month. Discounting the €0.5 with the current spot rate SR(0,6) will give you the value of the swap: 0.5/(1+0,08/2)^0.5 = 0,5/1.019803903 = 0.49 If you receive the fixed-rate and pay the variable rate the value is negative (€-0.49) and vice versa.

(b) What should be the swap rate such that the price of this swap is zero?

The yield curve including the 6M EURIBOR must be totally flat, i.e. the first 6M EURIBOR rate must be 8%.

Regards, Oscar

Be careful with your language. I suspect that you mean that the _ value _ of this swap is zero.

The _ price _ of a swap is the fixed rate. So, the way your question is posed, the answer is _ 0% _.

Thanks Magician!

I got it wrong to. The corresponding Swap rate (fixed-rate w/o margin) would be:

Swap-rate = (((1+0,045)*(1+0,04)*(1+0,04)*(1+0,04)*(1+0,04)*(1+0,04)*(1+0,04)*(1+0,04))^1/8 - 1)*2 = ((1+0,045)*(1+0,04)^7)^1/8 - 1)*2 = 0.81247 = 8.125%

First of all, I would like to express my gratitude for Oscar and S2000magician. Guys you have helped me a lot with your answers lately, however I have one more doubt… If the therm structure would be increasing , let’s say 10% © and in other case decreasing 7% (d) how would the answer change ? the

In case of increasing the values would change by:

FIXED FLOATING YR0.5 4/(1+0,1)^(1/2) YR0.5 4.5/(1+0,1)^(1/2) YR1.0 4/(1+0.1)^1 … … YR4.0 4/(1+0.1)^4 YR4.0 4.5/(1+0.1)^4

Thus, the decreasing would have been calculated with as well, just with 7% ? Any ideas ?