# Market Value of an Interest Rate Swap

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.

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?

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

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?

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

Thanks @MikeyF