Fixed-rate receiver

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. 

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. 

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... 

In contrast, the fixed-rate receiver must make payments with a present value of 11,459,495, but will only receive fixed-rate payments with a present value equal to 9,473,390. Thus, the value of the swap for the fixed-rate receiver is - 1,986,105. Again, as explained earlier, the fixed-rate receiver is adversely affected by a rise in interest rates because it results in a decline in the value of a swap. 

Since the product Dk is known from the steady state rate of permeation, kp can also be obtained. This time lag method is the basis of most of the gas and some of the vapor transport studies made today. Little application of the time lag method was made until Barter introduced the use of vacuum on the downstream side of the membrane and measured the gas permeation rate by monitoring the increase in pres-arre in a fixed downstream receiving volume Recently the original isobaric method has been reintroduced in a number of commercial permeability instruments. 

Per diem The MCO negotiates with a provider organization (e.g. accredited hospitals, ambulatory care centers, etc.), who agrees to deliver care for a fixed rate per day that an enrollee receives care. 

In other words, if market interest rates rise, the mark-to-market (mtm) value of a receive-fixed swap will be increasing as discounting rates rise. In turn, this means that the break-even rate of the swap moves lower hence a market making swap bank will require a lower fixed rate if it is to price the swap correctly as discounting rates rise. 

Strictly speaking, the FIAT 1 transaction does not generate excess spread. This explains the high level of credit enhancement from the unrated class M notes (usually, unrated tranches are either privately sold or kept as an equity tranche by the originator). On the closing date, an amount of notes was issued which was equal to the net present value of all future cash payments due from the collateral (as opposed to the principal balance of the collateral). The discount rate used was the fixed rate payable to the swap counterparty (swap rate plus coupon on the class A notes and all fees associated with the transaction). Structured this way, the receivables always yield the discount rate, leaving no excess spread in the transaction. However, losses on the FIAT 1 portfolio can be covered to a certain degree from interest collections because the structure provides for delinquent principal and defaults to be covered before interest is paid on the class M notes. 

One solution to this problem, of course, is for the company to enter into a 5-year interest rate swap on a notional principal of 1 million, agreeing to pay the fixed rate and receive the floating rate. In our illustration, the fixed rate might be 3%, in which case the company would effectively lock into paying the fixed rate of 3% per annum over the 5-year period. While this protects the company against higher interest rates, the company cannot benefit from lower rates, especially at the outset when rates are just 2%. 

A receivers swaption grants the holder the right to receive the fixed rate in the underlying swap. 

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%. 

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. 

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... 

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. 

Investors can also use interest rate swaps for a similar purpose. These contracts exchange fixed-rate cash flows for floating-rate cash flows based on LIBOR/EURIBOR. Investors on the paying (fixed) leg of the swap reduce the duration of their portfolio, while those on the receiving (fixed) leg increase the duration of the portfolio. Since interest rate swaps are extremely liquid contracts, they are an efficient way of expressing a short-term view on interest rates. 

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. 

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