Interest rate swaps and derivatives

2 free worked examples

Solved in full, free to everyone, and never rotated. Read these before deciding whether the rest of the drill is worth paying for.

1. Exam FMInterest rate swaps and derivativesExam level

   Annual spot rates are 4%, 4.6% and 5.1%. Find the 3-year annual swap rate on a notional of 1.

   1. A$4.6000\%$
   2. B$5.0000\%$
   3. C$5.0651\%$
   4. D$5.1000\%$
   5. E$5.5000\%$

   Solution

   1. The swap rate is $R=\frac{1-P(n)}{{\sum }_{t}P(t)}$, where $P(t)$ are the zero-coupon prices.
   2. $P(1)=0.961538$, $P(2)=0.913980$, $P(3)=0.861374$, summing to $2.736893$.
   3. $R=\frac{1-0.861374}{2.736893}=\frac{0.138626}{2.736893}$.
   4. $=5.0651\%$, just below the 3-year spot rate - a swap rate is a PV-weighted average of the forwards, so it lags the longest spot on a rising curve.

   Trap. Averaging the spot rates rather than working with the discount factors.

2. Exam FMInterest rate swaps and derivativesExam level

   A borrower with floating-rate debt wants certainty of payments. Which swap position achieves it?

   1. AReceive fixed, pay floating
   2. BPay fixed, receive floating
   3. CBuy a floating-rate note
   4. DSell a fixed-rate bond
   5. ENothing in the swap market helps

   Solution

   1. The borrower already PAYS floating on its debt.
   2. Entering a swap to RECEIVE floating offsets that exposure, and the swap's fixed leg becomes the borrower's net obligation.
   3. So the position needed is pay fixed, receive floating - a payer swap.
   4. The combination synthesises a fixed-rate loan without renegotiating the original debt.

   Trap. Choosing the receiver swap, which doubles the floating exposure rather than removing it.