# How to calculate a forward-starting swap with forward equations?

I have been trying to resolve this problem for some time but I cannot get the correct answer. The problem is the following one.

Compute the initial value of a forward-starting swap that begins at $t=1$, with maturity $T=10$ and a fixed rate of 4.5%. (The first payment then takes place at $t=2$ and the final payment takes place at $t=11$ as we are assuming, as usual, that payments take place in arrears.) You should assume a swap notional of 1 million and assume that you receive floating and pay fixed.)

We also know that

• $r_{0,0}=5\%$
• $u=1.1$
• $d=0.9$
• $q=1−q=1/2$

Using forward equations from $t=1$ to $t=9$, I cannot resolve the problem:

Here is what I have done in Excel with a final result of -31076 but it is not the correct answer: • So you're trying to compute the value of the swap at $t=0$ is that right? – SRKX Nov 27 '14 at 1:43
• Yes, I am trying to calculate the inital value of the swap and I thought that it had a total value of 31076 but it is not the correct result – Katherine99 Nov 27 '14 at 8:48
• why do you need a tree? You already have the cash flows on the fixed leg; for the floating leg, just project the cash flows using LIBOR forwards. Calculate the PV of both legs and you're done. – Helin Dec 28 '14 at 21:33
• I've done pretty much the same thing that you have except that I don't understand why you have taken the sum from t=1 to t=9. When I have summed up the elementary price equations for the forward swap I obtained a value of -38136 which is the same answer I retrieved through risk neutral pricing But even then, my answer is wrong. So I am really stumped. I've been trying for a lot of time and am not making any headway. If you have figured out the solution by now, please let me know the methodology you have adopted. – Uma Maheshwar Reddy Jul 27 '15 at 11:01