Market Value of an Interest Rate Swap

CFA Level II Derivatives
#1

Hi folks,

Here is the relevant data for the question:

  • Notional amount = $5 million
  • Swap is one-year with quarterly settlement
  • Swap fixed rate at initiation is 4.4%
  • After 180 days, MRR term structure is flat at 3.5% over the next year

The question then asks us to calculate the value of the swap to the fixed-rate receiver.

Here is the answer given:

image
image839×424 59.1 KB

Two clarifications I need:

  1. Why must the new swap fixed rate be 3.5%, if the MRR term structure is flat at 3.5% ?
  2. In this computation below, why do we use 90 days instead of 180 days in the numerator when adjusting the % to a per-period basis?
    image

Thanks in advance!

#2

  1. We work out fixed rate on swap by think what will coupon be on a bond selling at par given current spot rates. As discount rates are flat. Coupon = rate if bond sells at par.

  2. It is quartely settlement on the swap.
    Each theoretical payment would be (3.5% - 4.4%) x (90/360) x $5m if we closed out the swap
    The 1.9741 is the discount factor

#3

Thanks @MikeyF

Just to clarify:

  1. Are we saying the swap fixed rate is always equal to the coupon rate of a bond selling at par, based on the corresponding maturity/settlement date?
#4

That is how we calaculate the rate assuming no arbitrage possibilities.

The market may offer slighly different prices but if it moves too far away arbitrage possibilities will exist

#5

Thanks @MikeyF