Fixed-rate payer

A payers swaption grants the holder the right to enter into the underlying swap as the fixed-rate payer. 

The buyer of this swaption has the right, one year from now, to enter into a 3-year swap as the fixed-rate payer, paying 4% p.a. against receiving 3-month EURIBOR, on a notional principal of 10 million. If 3-year swap rates on 29 March 20X4 were, say, 4.5%, it would be worthwhile for the owner to exercise the swaption, paying a fixed rate of only 4% when the market rate was 4.5%. 

Cancellable swaps—which can be cancelled by one party prior to the scheduled termination date. For example, the party with the cancellation right may elect to do so if he or she was the fixed-rate payer and... 

Extendible swaps—which can be extended by one party beyond the scheduled termination date. In this case, the party with this ability may choose to extend a 3-year swap to five years if they were the fixed-rate payer, and rates had risen substantially. 

Reversible swaps—which allow one party to reverse the direction of the swap. For example, the party could switch from being the fixed-rate payer to being the fixed-rate receiver. This might happen if a company was able to repay its borrowing prematurely, was now a net investor, and rates had fallen substantially. 

If 2-year rates rise sufficiently in 3-years time, the swaption will expire in-the-money, and the investor can exercise the payer s swaption, entering into a second swap as the fixed-rate payer at exactly the same rate as the original swap, for which the investor is the fixed-rate receiver. This second swap exactly offsets the first swap, effectively cancelling the original swap for the last two years of its life. 

It can be seen from the net cash flow in Exhibit 19.1 that a fixed-rate payer has a cash market position that is equivalent to a long position in a floating-rate bond and a short position in a fixed-rate bond— the short position being the equivalent of borrowing by issuing a fixed-rate bond. 

While our illustrations assume that the timing of the cash flows for both the fixed-rate payer and floating-rate payer will be the same, this is rarely the case in a swap. An agreement may call for the fixed-rate payer to make payments annually but the floating-rate payer to make payments more frequently (semi-annually or quarterly). Also, the way in which interest accrues on each leg of the transaction differs, because there are several day count conventions in the fixed-income markets as discussed in Chapter 3. 

The terminology used to describe the position of a party in the swap markets combines cash market jargon and futures market jargon, given that a swap position can be interpreted as a position in a package of cash market instruments or a package of futures/forward positions. As we have said, the counterparty to an interest rate swap is either a fixed-rate payer or floating-rate payer. Exhibit 19.2 describes these positions in several ways. 

Fixed-Rate Payer Floating-Rate Payer... 

The offer price that the dealer would quote the fixed-rate payer would be to pay 8.85% and receive EURIBOR flat. (The word flat means with no spread.) The bid price that the dealer would quote the floating-rate payer would be to pay EURIBOR flat and receive 8.75%. The bid-offer spread is 10 basis points. 

The fixed rate is some spread above the benchmark yield curve with the same term to maturity as the swap. In our illustration, suppose that the 10-year benchmark yield is 8.35%. Then the offer price that the dealer would quote to the fixed-rate payer is the 10-year benchmark rate plus 50 basis points versus receiving EURIBOR flat. For the floating-rate payer, the bid price quoted would be EURIBOR flat versus the 10-year benchmark rate plus 40 basis points. The dealer would quote such a swap as 40-50, meaning that the dealer is willing to enter into a swap to receive EURIBOR and pay a fixed rate equal to the 10-year benchmark rate plus 40 basis points and it would be willing to enter into a swap to pay EURIBOR and receive a fixed rate equal to the 10-year benchmark rate plus 50 basis points. 

In an interest rate swap, the counterparties agree to exchange periodic interest payments. The euro amount of the interest payments exchanged is based on the notional principal. In the most common type of swap, there is a fixed-rate payer and a fixed-rate receiver. The convention for quoting swap rates is that a swap dealer sets the floating rate equal to the reference rate and then quotes the fixed rate that will apply. 

In the previous section we described in general terms the payments by the fixed-rate payer and fixed-rate receiver but we did not give any details. That is, we explained that if the swap rate is 6% and the notional amount is 100 million, then the fixed-rate payment will be 6 million for the year and the payment is then adjusted based on the frequency of settlement. So, if settlement is semiannual, the payment is 3 million. If it is quarterly, it is 1.5 million. Similarly, the floating-rate payment would be found by multiplying the reference rate by the notional amount and then scaled based on the frequency of settlement. 

At the inception of the swap, the terms of the swap will be such that the present value of the floating-rate payments is equal to the present value of the fixed-rate payments. That is, the value of the swap is equal to zero at its inception. This is the fundamental principle in determining the swap rate (i.e., the fixed rate that the fixed-rate payer will make). 

Suppose that today 3-month EURIBOR is 4.05%. Let s look at what the fixed-rate payer will receive on 31 March of year 1—the date when the first quarterly swap payment is made. There is no uncertainty about what the floating-rate payment will be. In general, the floating-rate payment is determined as follows ... 

In our illustration, assuming a nonleap year, the number of days from 1 January of year 1 to 31 March of year 1 (the first quarter) is 90. If 3-month EURIBOR is 4.05%, then the fixed-rate payer will receive a floating-rate payment on March 31 of year 1 equal to... 

We will begin with the next quarterly payment—from 1 April of year 1 to 30 June of year 1. This quarter has 91 days. The floating-rate payment will be determined by 3-month EURIBOR on 1 April of year 1 and paid on 30 June of year 1. Where might the fixed-rate payer look to today... 

Exhibit 19.6 shows the present value for each payment. The total present value of the 12 floating-rate payments is 14,052,917. Thus, the present value of the payments that the fixed-rate payer will receive is 14,052,917 and the present value of the payments that the fixed-rate receiver will make is 14,052,917. 

The fixed-rate payer will require that the present value of the fixed-rate payments that must be made based on the swap rate not exceed the 14,052,917 payments to be received from the floating-rate payments. The fixed-rate receiver will require that the present value of the fixed-rate payments to be received is at least as great as the 14,052,917 that must be paid. This means that both parties will require a present value for the fixed-rate payments to be 14,052,917. If that is the case, the present value of the fixed-rate payments is equal to the present value of the floating-rate payments and therefore the value of the swap is zero for both parties at the inception of the swap. The interest rates that should be used to compute the present value of the fixed-rate payments are the same interest rates as those used to discount the floating-rate payments. 

Fixed-Rate Payer Fixed-Rate Receiver... 

The fixed-rate payer will receive the floating-rate payments. And these payments have a present value of 11,459,495. The present value of the payments that must be made by the fixed-rate payer is 9,473,390. Thus, the swap has a positive value for the fixed-rate payer equal to the difference in the two present values of 1,986,105. This is the value of the swap to the fixed-rate payer. Notice, when interest rates increase (as they did in the illustration analyzed), the fixed-rate payer benefits because the value of the swap increases. 

Interest rate swaps trade in a secondary market, where their values move in line with market interest rates, just as bonds values do. If, for instance, a 5-year interest rate swap is transacted at a fixed rate of 5 percent and 5-year rates subsequently fall to 4.75 percent, the swap s value will decrease for the fixed-rate payer and increase for the floating-rate payer. The opposite would be true if 5-year rates moved to 5.25 percent. To understand why this is, think of fixed-rate payers as borrowers. If interest rates fall after they settle their loan terms, are they better off No, because they are now paying above the market rate on their loan. For this reason, swap contracts decrease in value to the ftxed-rate payers when rates fall. On the other hand, floating-rate payers gain from a fall in rates, because... 

There is no net outflow or inflow at the start of these trades, because the 100 million spent on the purchase of the FRN is netted with the receipt of 100 million from the sale of the Treasury. The subsequent net cash flows over the three-year period are shown in the last column. As at the start of the trade, there is no cash inflow or outflow on maturity. The net position is exactly the same as that of a fixed-rate payer in an interest rate swap. For a floating-rate payer, the cash flow would mirror exactly that of a long position in a fixed-rate bond and a short position in an FRN. Therefore, the fixed-rate payer in a swap is said to be short in the bond market—that is, a borrower of funds—and the floating-rate payer is said to be long the bond market. 

In this example, the bank is quoting an offer rate of 5-25 percent, which is what the fixed-rate payer will pay, and a bid rate of 5-19 percent, which is what the floating-rate payer will receive. The bid-offer spread is therefore 6 basis points. The fixed rate is always set at a spread over the government bond yield curve and is often quoted that way. Say the 5-year Treasury is trading at a yield of 4.88 percent. The 5-year swap bid and offer rates in the example are 31 basis points and 37 basis points, respectively, above this yield, and the bank s swap trader could quote the swap rates as a swap spread 37-31. This means that the bank would be willing to enter into a swap in which it paid 31 basis points above the benchmark yield and received LIBOR or one in which it received 37 basis points above the yield curve and paid LIBOR. 

A bank or corporation may buy or sell an option on a swap, known as a swaption. The buyer of a swaption has the right, but not the obligation, to transact an interest rate swap during the life of the option. An option on a swap where the buyer is the fixed-rate payer is termed a call swaption one where the buyer becomes the floating-rate payer is aswaption. The writer of the swaption becomes the buyers counterparty in underlying the transaction. 

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