For example, 1 year ago, company A issues a 4-year 5% coupon bond.

At the present (t=0), company A wants to convert that fixed coupon bond into floating rate bond → so he can short IRS with Notional amount = face value of bond.

Here are spot rate at t=0

s1=2.3960% s2=3.4197% s3=4.0005%

Based on this information, we can calculate FIXED SWAP RATE = 3.964%

There is mistmatch between Fixed swap rate and coupon rate.

Is there anyway for company A to float the fixed rate ?

Theroretically they can eneter a swap.

Various points.

What is the ytm of the bond now?

Assuming price is still par and YTM > swap rate

is the swap rate quoted based on risk free rates? The company is a risky borrower.

The swap dealer is unlikely to quote 3.964% to company A if they ask for a swap.

Suppose that the principal amount of the bond is $P.

The bond pays an annual coupon of 5% and has a life of 4 years.

So the coupon payments are 5/100 * P

According to you, a 4 year flxed-for-floating swap has a swap-fixed-rate of 3.964%.

Swaps with a notional amount of 5/3.964 * P = 1.261352170 P will replicate the coupon payments of the bond.

However, company enters a Swap with Notional amount =1.261352170P, so they have to pay Floating rate based on Notional amount = 1.261352170P > Face value = P.

This swap is not equivalent to an FLOATING RATE BOND with FV=100?

s1,s2, and s3 is the spot rate of A bonds

You should think about what the company is trying to do.

With a pay-fixed,receive-floating swap, the company exchanges a series of fixed payments for a series of floating payments.

The notional amount is not normally exchanged because it would be the same for both sides so there would be no point.

The company is currently receiving a stream of fixed payments of P*(5/100) a year for 4 years.

That’s all you know about the bond. You don’t know if it was issued at par, at a discount, or at a premium.

The company wants to swap that fixed payment stream for a floating payment stream.

The fixed leg of the arrangement I laid out replicates the fixed payment stream the company is currently receiving, which is what the company needs.

The fixed leg of a swap with a notional of P will only pay P*(3.964/100) a year for 4 years, which doesn’t replicate the payment stream of the bond.