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
*r0,0=5%, u=1.1, d=0.9 and 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:
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.
Edit: Okay, after a lot of head scratching I have finally figured out the answer.
Previously I had summed from t=0 to t=10. But as the question states that the swap needs to be priced from t=1 to t=10 with the payments beginning from t=2 and ending at t=11. Hence, we sum up the values as shown in your third tree from t=1 to t=10.
Also it is given that we receive floating rates and pay fixed rates. This leads to reversal of signs.
The correct answer I finally got is 33374.