An investor enters into a 4 year interest rate swap with a bank, agreeing to pay a fixed rate of 4% on a notional of $100m in return for receiving LIBOR. What is the value of the swap to the investor two years hence, immediately after the net interest payments are exchanged? Assume the current zero coupon bond yields for 1, 2 and 3 years are 5%, 6% and 7% respectively. Also assume that the yield curve stays the same after two years (ie, at the end of year two, the rates for the following three years are 5%, 6%, and 7% respectively).


$3,630,846


$2,749,326


-$2,749,326


- $3,630,846


Your Answer is Incorrect

The correct answer is choice 'a'

The swap can be valued by valuing the two individual components of the swap.

The fixed rate bond equivalent in the swap is valued at =4/1.05 + 104/(1.06^2) = $96,369,154.
The FRN component will be valued at par as we are at a point where the rate has just been reset, ie $100m.

The investor is paying the fixed rate, and is therefore short the bond. He/she is receiving LIBOR, and is therefore long the FRN. The value of the swap to the investor therefore is +$100,000,000-$96,369,154 = $3,630,846
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Is this correct, why is the notional for the fix leg discounted and the notional for floating is not?

Best,
Gracjan