On July 1st, 2010 the term structure of Euribor interest rates is expressed through the
discount factors in the following table:
| t (years) | S(t) |
| 0.5 | 0.99751 |
| 1 | 0.99354 |
| 1.5 | 0.98753 |
| 2 | 0.97836 |
| 2.5 | 0.96942 |
| 3 | 0.96256 |
a) Calculate the fair swap rate for a 2-year swap with annual payments for both
the floating and the fixed leg.
b) Calculate the annualized forward rate between 1 year and 1.5 years.
c) Prove formally that the present value of all floating leg payments for a swap
with maturity n (with no final payment of the notional) is equal to 1-S(n).
d) Calculate the fair swap rate for a 2-year forward start swap beginning at the
end of year 1 and maturing at the end of year 3, with annual payments for the
fixed leg and semi-annual payments for the floating leg.
e) Consider a 3-year cap composed by 3 one-year caplets. The cap rate is 1.60%.
How many of the three caplets are currently in-the-money (i.e. have a positive
intrinsic value at present)?
f) The fair swap rate for a 4-year swap with annual payments of the fixed leg is
1.80%. Calculate the 4-year zero coupon rate.
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