EURIBOR rates

Although the 2.59% floor may be slightly above the prevailing EURIBOR rate of 2% at the outset, the company may be quite prepared to hedge at this level, expecting as it does that rates will rise substantially. 

EURIBOR rates with maturities between one month and one year. 

We consider EURIBOR rates with maturities ranging from one day to one year. These rates, expressed on an actual/360 basis, are first converted into equivalent zero-coupon rates on an Actual/365 basis. Eor example, on 1 January 1999, the 1-month EURIBOR rate was equal to 2.5%. Using the Actual/365 basis, the equivalent zero-coupon rate (denoted by R(0,l/12)) is given by... 

The Calculation Agent s main role is to determine the EURIBOR rate and calculate and notify all relevant parties of the interest amounts owing to the Noteholders on each Interest Payment Date. The Calculation Agent will be part to the Agency Agreement. 

FRNs can have additional features, such as flbors, which specify minimum levels below which the coupon cannot fall caps, which specify maximum rates and calls, which specify possible redemption dates before maturity. Perpetual FRNs also exist. As in other markets, borrowers frequently issue floating notes with specific, even esoteric, terms to meet particular requirements or customer demands. For example. Citibank issued a series of U.S. dollar—denominated FRNs indexed to the Euribor rate and another set of notes whose day count was linked to a specified LIBOR range. 

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. 

In contrast to a conpon rate that remains unchanged for the bond s entire life, a floating-rate security or floater is a debt instrument whose coupon rate is reset at designated dates based on the value of some reference rate. Thus, the coupon rate will vary over the instrument s life. The coupon rate is almost always determined by a coupon formula. For example, a floater issued by Aareal Bank AG in Denmark (due in May 2007) has a coupon formula equal to three month EURIBOR plus 20 basis points and delivers cash flows quarterly. 

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. 

Floating-rate notes (FRNs) are Eurobonds that have their coupon levels reset periodically, with reference to a money market rate. For dollar-denominated assets, this is LIBOR (the London Inter-bank Offer Rate) as determined by a group of 16 reference banks. The mechanism is run by the British Bankers Association (BBA). The BBA also supervises LIBOR fixings in a number of other currencies. For euros, the most common reference rate is EURIBOR, as determined by a reference group of around 50 banks chosen by European Banking Federation. In both cases, most issues are priced off of the three-month rate, although one-month and six-month rates are also used. 

During 2002 Bund GC traded in a range around 2-10 basis points below EURIBOR in the short dates, while on occasion trading in specials went down to 90 basis points below the GC rate. As in other markets, there are a number of reasons why government stocks become special in the German market however, the primary factor is the extent of its deliverability into the Bund futures contract. For illustration we show, in Exhibit 10.23, the spread below GC for repo in the DBR... 

The EURIBOR futures contract provides the buyer with the theoretical commitment to place 1 million on deposit at a fixed interest rate for a nominal 90-day period starting on the futures expiry date, the third Wednesday of the delivery month. The fixed interest rate is not quoted directly, but is defined as 100 minus the quoted futures price. So if an investor buys a future at a price of 97, he or she is theoretically committed to deposit 1 million at 3% for 90 days. We have twice used the word theoretically because, in practice, these futures contracts are always cash settled, which means that buyers and sellers effectively pay or receive the difference between ... 

So if an investor bnys one EURIBOR futnres contract at 97.000, implying a 3% rate of interest, and the contracts expire at 97.500, implying a 2.5% interest rate, the investor receives... 

An alternative solution is for the company to buy a 5-year interest rate cap on 6-month EURIBOR. Exhibit 17.17 illustrates the effect of such a cap if the strike price were set at 3%. 

In any 6-month period when the EURIBOR setting is below 3%, the interest rate cap struck at 3% is out-of-the-money and does not affect the borrower, who can benefit from the lower rates, especially at the outset. However, whenever EURIBOR fixes above 3%, the interest rate cap pays the difference between the 3% strike rate and the rate prevailing. For example, if EURIBOR fixed at 4%, the company would receive 5,000 from the cap counterparty (assuming a 180-day period), and this sum would bring the effective EURIBOR down from 4% to 3% for that period. 

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 diagram highlights for each caplet the difference between the option period and the protection period. For example, the last caplet has a 4.5 year option period during which interest rates can vary and expose the company to risk. When the caplet expires, the caplet provides compensation over the 6-month protection period if the EURIBOR setting at the outset of that period exceeds the strike rate. 

You can see why a cap is actually a combination of single-period options by thinking about what happens every six months. In our example, the expiry dates of the nine caplets are set to coincide with the company s EURIBOR setting dates. Six months after the loan commences, the rate for the second interest period will be set by reference to the EURIBOR fixing that day. On the same date, the first caplet expires. If EURIBOR is above the strike rate of 3%, the company will exercise the caplet and receive compensation if EURIBOR is lower, the company will simply let the caplet expire worthless. The same process will apply six months later, and so on. 

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%. 

A capped note is like a regular floating-rate note (FRN), but paying an enhanced return subject to an absolute cap on interest rates. For example, with 6-month EURIBOR currently at 2%, a regular 3-year FRN issued by XYZ Corp might pay 6-month EURIBOR plus 40 bp. A 3-year capped note from XYZ might pay 6-month EURIBOR plus 50 bp, subject to a maximum rate of 3.5%. 

A floored note is similar to a capped note, except that the investor is promised a minimum interest rate. Continuing the previous example, XYZ might offer its investors a 3-year floored note paying 6-month EURIBOR plus 38 bp, with a guaranteed minimum rate of 2.38%. This promises the investor that the return can never fall below the initial prevailing rate. 

In this case the investor has effectively bought from XYZ a 3-year floor on 6-month EURIBOR struck at 2% for an up-front premium of around 2 bp (very cheap), equivalent to less than 1 bp p.a. over three years. XYZ deducts 2 bp from its normal EURIBOR margin to offer investors a slightly lower yield of EURIBOR plus 38 bp right now, in return for guaranteeing that the rate cannot fall any lower. XYZ uses 1 bp of the 2 bp deduction to buy the 3-year floor (perhaps from a bank), and keeps the other 1 bp itself. 

These notes accrue interest daily at an enhanced yield, provided that a particular market rate falls within a specified range. For example, when the 1-year yield on vanilla instruments is 4%, a dollar-denominated, 1-year range accrual note might accrue interest at 6% p.a. on every day that 3-month EURIBOR fixes in the range 2.5% to 3.5%, otherwise it accrues nothing that day. 

With a little arithmetic, you can see that the coupon on the structured note will be EURIBOR plus 70 bp, so long as rates stay below 4.50%. This is an enhanced return. If rates rise above 4.50%, however, the investor s return falls substantially, reaching 0% if EURIBOR reaches 5.80%. This note would appeal to the investor who thought that rate would rise from their current levels of 2%, but not beyond 4.5%. 

The structure is achieved by XYZ effectively buying 5-year caps struck at 4.50% on five times the notional principal of the note issued. Eor example, if XYZ issued notes with a face value of 10 million, it would effectively buy interest rate caps from investors with a notional principal of 50 million. The up-front premium of 19 bp in this example, therefore, becomes geared up to 95 bp, equivalent to 20 bp p.a. This enables the investor to receive their enhanced coupon, but the geared payment from the caps sold means that investors return diminishes rapidly in any period where EURIBOR sets above 4.50%. 

Take, for example, a borrower who needs protection against unexpected rises in interest rates over the course of a 5-year loan. EURIBOR might be low right now but, in a rising yield-curve environment, may increase significantly over time. For example, 6-month EURIBOR might currently be 2%, but 6-month forward rates may rise to 5% in the last six months of a 5-year loan. A cap struck at 4% would be well out-of-the-money in early periods, but well in-the-money for later periods. 

For example, suppose the ratchet cap initially had a strike rate of 3%, and a spread of 50 bp. So long as EURIBOR stayed below 3%, the caplets would expire out-of-the-money, and the strike rate would remain at 3%. The first time that EURIBOR sets above 3%, however, the expiring caplet would result in a payment to the owner of the cap, but the strike rates for all the remaining caplets would be reset to 3.5%. The cap would therefore not pay out again until rates rose to this higher level, whereupon the strike rate would be ratcheted up to 4%, and so on. 

This structured derivative is best illustrated by an example. Suppose that, when 6-month EURIBOR was 3%, a borrower purchased a knockout cap with a strike rate of 5%, and a knock-out rate of 1.75%. This cap would behave normally provided EURIBOR stayed above 1.75%. If, however, EURIBOR traded down to 1.75% or lower, the cap would be permanently knocked out, and would provide no further protection, even if rates subsequently rose above 5%. 

A knock-in cap works in an analogous way, except that the barrier has to be hit for the cap to be activated. As an example, consider a knock-in version of the 5-year cap struck at 5%, with a knock-in rate of 1.75%. The borrower would pay a reduced premium, but the cap would be ineffective until and unless EURIBOR first fell to 1.75%. Once that happened, the cap would be knocked in, and thereafter would behave... 

Let s now turn our attention to look at situations where interest rate options are used to hedge against changes in interest rates. To illustrate this, we will consider the case of a company that is borrowing 10 million at 6-month EURIBOR plus 1% for a 5-year period, with the interest rate reset every six months. The floating rate for the first period has just... 

As the chart shows, the company s unhedged cost is simply 1% over EURIBOR, reflecting the company s 1% credit margin. With the collar in place, the company s borrowing costs are unaffected when EURIBOR resets in-between the strike rates of 2.59% and 4%. This is because the collar has a zero cost, and neither the cap nor the floor are exercised when EURIBOR stays within this range. If, however, EURIBOR exceeds 4%, the cap compensates the company for the excess interest paid, capping the effective cost at 5%. Similarly, if EURIBOR fixes below 2.59%, the company s borrowing costs are floored at 3.59%. 

If EURIBOR sets above the strike rate of 3.5%, the cap purchased by the company limits the effective borrowing cost to 4.5%, 1% above the cap strike, while the floor for that period expires out-of-the-money. The company s maximum borrowing rate is therefore capped, in the same way as with a zero-cost collar. 

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. 

If daily fixings of 3-month EURIBOR over the next year stay in the range 2.00% to 3.50%, the investor will receive an enhanced yield of 6.75% p.a. on a structured note, this coupon being paid as a single annual payment on the maturity of the note. This compares well with the 4.50% one year rate currently available on vanilla notes of similar credit quality. 

Euronext-LIFFE s 3-month EURIBOR futures option, traded on the Chicago Mercantile Exchange, is an actively traded short-term interest rate option that enjoys high trading volume. If these options are exercised, the buyer and the seller of the option take positions in an underlying 3-month EURIBOR futures contract. The futures contract is cash-settled and the final price at delivery is equal to 100 minus the 3-month LIBOR. 

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-... 

Buy 50 million par value of a 5-year floating-rate bond that pays 6-month EURIBOR every six months. 

The cash flows for this transaction are set forth in Exhibit 19.1. The second column of the exhibit shows the cash flows from purchasing the 5-year floating-rate bond. There is a 50 million cash outlay and then 10 cash inflows. The amount of the cash inflows is uncertain because they depend on future levels of 6-month EURIBOR. The next column shows the cash flows from borrowing 50 million on a fixed-rate basis. The last column shows the net cash flows from the entire transaction. As the last column indicates, there is no initial cash flow (no cash inflow or cash outlay). In all 10 6-month periods, the net position results in a cash... 

The subscript for EURIBOR indicates the 6-month EURIBOR as per the terms of the floating-rate bond at time t. 

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