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:

enter image description here

  • $\begingroup$ So you're trying to compute the value of the swap at $t=0$ is that right? $\endgroup$
    – SRKX
    Nov 27, 2014 at 1:43
  • $\begingroup$ 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 $\endgroup$ Nov 27, 2014 at 8:48
  • 3
    $\begingroup$ 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. $\endgroup$
    – Helin
    Dec 28, 2014 at 21:33
  • $\begingroup$ 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. $\endgroup$ Jul 27, 2015 at 11:01

1 Answer 1


You have to use T=1...10 because last payment is discounted to year 10. So your short rate lattice is incomplete.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.