Floating-rate payments determination

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). 

For the first floating-rate payment, the amount is known. For all subsequent payments, the floating-rate payment depends on the value of the reference rate when the floating rate is determined. To illustrate the issues associated with calculating the floating-rate payment, we will assume that... 

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 ... 

Now let s return to our objective of determining the future floating-rate payments. These payments can be locked in over the life of the swap using the EURIBOR futures contract. We will show how these floating-rate payments are computed using this contract. 

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... 

Note that each futures contract is for 1 million and hence 100 contracts have a notional amount of 100 million.) Similarly, the EURI-BOR futures contract can be used to lock in a floating-rate payment for each of the next 10 quarters. Once again, it is important to emphasize that the reference rate at the beginning of period t determines the floating rate that will be paid for the period. However, the floating-rate payment is not made until the end of period t. 

In our illustration we will assume that the frequency of settlement is quarterly for the fixed-rate payments, the same as with the floating-rate payments. The day count convention is the same as for the floating-rate payment, actual/360. The equation for determining the euro amount of the fixed-rate payment for the period is... 

It is the same equation as for determining the floating-rate payment except that the swap rate is used instead of the reference rate (3-month EURIBOR in our illustration). 

Let s apply the formula to determine the swap rate for our 3-year swap. Exhibit 19.7 shows the calculation of the denominator of the formula. The forward discount factor for each period shown in Column (5) is obtained from Column (4) of Exhibit 19.6. The sum of the last column in Exhibit 19.7 shows that the denominator of the swap rate formula is 281,764,282. We know from Exhibit 19.6 that the present value of the floating-rate payments is 14,052,917. Therefore, the swap rate is... 

Once the swap transaction is completed, changes in market interest rates will change the payments of the floating-rate side of the swap. The value of an interest rate swap is the difference between the present value of the payments of the two sides of the swap. The 3-month EURIBOR forward rates from the current EURIBOR futures contracts are used to (1) calculate the floating-rate payments and (2) determine the discount factors at which to calculate the present value of the payments. 

Moreover, duration will be influenced by the floater s stmcture. In fact, the choice of the reference rate affects the duration depending on how much volatile the index is. The lower the frequency of couptm payments, the greater the price sensitivity between reset dates. Thus, while floating-rate notes have a lower price sensitivity to a change of the reference rate, fixed and floating-rate notes both have a price sensitivity to changes of credit spread reflecting the issuer s creditworthiness. A shift of the credit term structure will determine the decline of the bond s price. 

Investors should also determine the basis on which the DSCR level has been calculated. For example, does it include principal payments Where the borrower pays principal from year two, has this been factored in or has the level been calculated using interest payments only Also, what interest rate has been factored into the calculation the current floating rate or a more sustainable longer-term interest rate ... 

---