EURIBOR swapping

We consider three-or-six-month EURIBOR swap yields with maturities ranging from one year to 10 years and find recursively equivalent zero-coupon rates. Swap yields are par yields so the zero-coupon rate with maturity two years R(0,2) is obtained as the solution to the following equation ... 

As introduced, the reference rate represents the interest rate or index used to obtain the linkage. In the European market, the major parts of floating-rate note issuances are linked to the Euribor and the remaining to the constant maturity swap. In the US and UK markets, they are tied to the Libor and short-term treasury bonds. 

That said, there are two reasons why the performance of German swap spreads are related to Euro peripheral spreads. The first one is that, flows apart, the bond-swap spread reflects the yield difference between a government rate and the composition of a string of EURI-BOR rates (i.e., a swap fixed rate). As the average credit quality of the banks in the EURIBOR panel is A-AA, any increase in the investors preference for credit quality will make both swap and peripheral spreads widen versus the core Euro government rate, thus increasing the correlation between both differentials. Yet this increase in the correlation will be mainly due to the outperformance of the benchmark asset... 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

In this way, an interest rate cap allows the borrowing company to benefit when interest rates are low, while protecting the company when interest rates are high. This is marvellous, as it provides the best of both worlds, but such a result does not come free As with other interest rate options, the company would have to pay an up-front premium to purchase the cap. In the example here, this up-front premium might be around 165 bp of the notional principal, i.e., 16,500, which is equivalent to around 35 bp per annum if this cost were spread over the lifetime of the cap. This caps the effective EURIBOR at around 3.35% rather than 3%. Contrast this with the interest rate swap, which does not involve an up-front payment, but penalizes the company with a higher initial interest rate instead. 

The result for the company is that EURIBOR will effectively be collared in the range 2.50% to 3.50%. If EURIBOR ever rose above 3.50%, the company s costs would be capped at that level. The downside is that whenever the EURIBOR setting was below 2.50%, the company would not pay less. As neither the cap nor the collar include the first interest period, the company in this example is assured of six months borrowing based on a EURIBOR of 2%. Thereafter, even if EURIBOR were to stay low, the company s borrowing would be based on a EURIBOR of at least 2.50%. This may nonetheless still prove less expensive than paying the fixed rate of 3% throughout, which is what the swap would involve. 

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%. 

Suppose an investor has purchased a 5-year note paying 6-month EURIBOR plus 50 bp, with 6-month EURIBOR initially set at 2%. Interest rates are currently very low, so the investor is thinking about using a 5-year swap to boost the return. With 5-year swaps quoted at 3%, against EURIBOR flat, the investor could switch from 6-month EURIBOR plus 50 bp to an effective yield of 3.5%, enjoying an immediate 100 bp improvement in yield. This structure is pictured in Exhibit 17.30. 

The only problem with this strategy is that the investor cannot gain from any subsequent increase in EURIBOR. The swap freezes the yield to 3.5% for five years, regardless of what happens to EURIBOR in the future. 

The reference rates that have been used for the floating rate in an interest rate swap are various money market rates. The most common in Europe is EURIBOR. EURIBOR is the rate at which prime banks offer to pay on euro deposits available to other prime banks for a given maturity. There is not just one rate but a rate for different maturities. For example, there is a 1-month EURIBOR, 3-month EURIBOR, and 6-month EURIBOR. 

Consider the hypothetical interest rate swap nsed earlier to illustrate a swap. Let s look at party X s position. Party X has agreed to pay 10% and receive 6-month EURIBOR. More specifically, assuming a 50 million notional amount, X has agreed to buy a commodity called 6-month EURIBOR for 2.5 million. This is effectively a 6-month forward contract where X agrees to pay 2.5 million in exchange for deliv-... 

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 ... 

As explained earlier in this chapter, a swap position can be interpreted as a package of forward/futures contracts or a package of cash flows from buying and selling cash market instruments. It is the former interpretation that will be used as the basis for valuing a swap. In the case of a EURIBOR-based swap, the appropriate futures contract is the 3-month EURIBOR futures contract. For this reason, we will briefly describe this important contract. 

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. 

Exhibit 19.3 shows this for the 3-year swap. Shown in Column (1) is when the quarter begins and in Column (2) when the quarter ends. The payment will be received at the end of the first quarter (March 31 of year 1) and is 1,012,500. That is the known floating-rate payment as explained earlier. It is the only payment that is known. The information used to compute the first payment is in Column (4) which shows the current 3-month EURIBOR (4.05%). The payment is shown in the last column. Column (8). 

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). 

Now that we know how to calcnlate the payments for the fixed rate and floating-rate sides of a swap, where the reference rate is 3-month EURIBOR given (1) the cnrrent valne for 3-month EURIBOR (2) the expected 3-month EURIBOR from the EURIBOR futures contract and (3) the assnmed swap rate, we can demonstrate how to compnte the swap rate. 

We will refer to the present value of 1 to be received in period t as the forward discount factor. In our calculations involving swaps, we will compute the forward discount factor for a period using the forward rates. These are the same forward rates that are used to compute the floating-rate payments—those obtained from the EURIBOR futures contract. We must make just one more adjustment. We must adjust the forward rates used in the formula for the number of days in the period (i.e., the quarter in our illustrations) in the same way that we made this adjustment to obtain the payments. Specifically, the forward rate for a period, which we will refer to as the period forward rate, is computed using the following equation ... 

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. 

To illustrate this, consider the 3-year swap used to demonstrate how to calculate the swap rate. Suppose that one year later, interest rates change as shown in Columns (4) and (6) in Exhibit 19.8. In Colnmn (4) shows the current 3-month EURIBOR. In Column (5) are the EURIBOR futures price for each period. These rates are used to compute the forward rates in Column (6). Note that the interest rates have increased one year later since the rates in Exhibit 19.8 are greater than those in Exhibit 19.3. As in Exhibit 19.3, the current 3-month EURIBOR and the forward rates are used to compute the floating-rate payments. These payments are shown in Column (8) of Exhibit 19.8. 

Naturally, this presupposes the reference rate used for the floating-rate cash flows is EURIBOR. Furthermore, part of swap spread is attributable simply to the fact that EURIBOR for a given maturity is higher than the rate on a comparable maturity benchmark government. 

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. 

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