Chapter XV Eurocurrency Futures and Options Ch1

In Chapter XII, we were introduced to the Euromarkets. In that chapter, we briefly discussed the Eurocurrency market, which is a market for short-term deposits, or Eurodeposits. The most popular instrument in this market is the certificate of deposit (CD), which is a negotiable and often bearer instrument. We also mentioned that for long-term CDs (up to ten years), there is the possibility of selecting a CD with floating-rate coupons. For CDs with floating-rate coupons, the life of the CD is divided into subperiods of usually six months. The interest earned over such period is fixed at the beginning of the period, the reset date. This interest rate is based on the prevailing market interest rate at the time. In this chapter, we will describe the derivative instruments that have Eurocurrency instruments as the underlying asset. Then, we will focus on how to use those derivative instruments, especially Eurocurrency futures and options, to hedge interest rate risk. I. Eurocurrency Futures Eurocurrency futures are very simple futures contracts. To see this simplicity, consider a domestic futures contract on a time deposit (TD), where the expiration day of the futures (when the cash deposit is made), T1, precedes the maturity date T2 of the TD (when settlement occurs), by typically three months. The timing of the cash flows are shown in Exhibit XV.1. This futures TD contract locks you in a 3-mo. interest rate at time T1. Exhibit XV.1 Timing of a futures Time Deposit (TD) Example XV.1: In June you agree to buy in mid-September a TD that expires in mid-December. The value of the TD is 100, and the price you agree to pay is 96. The return you will realize on the TD during the last three months of its life is (100-96)/96 = 4.167% (or 16.67% on yearly basis). ¶ Eurocurrency futures work in the same way as the above mentioned time deposit futures. A Eurocurrency futures contract calls for the delivery of a 3-mo Eurocurrency time deposit at a given interest rate (LIBOR). Eurocurrency time deposits are the underlying asset in Eurocurrency futures. Actually, you can consider the interest rates (LIBOR) on the future Eurocurrency deposit as the underlying asset. The Eurocurrency futures contract should reflect the market expectation for the future value of LIBOR for a 3-mo deposit. Like with any other futures a trader can go long a Eurocurrency futures (an agreement to make a future XV.1 3-mo deposit) or short Eurocurrency futures (an agreement to take a future 3-mo. loan). A trader can go long a Eurocurrency futures -assuring a yield for a future 3-mo deposit- or go short a Eurocurrency futures -assuring a borrowing rate for a future 3-mo loan. Eurocurrency futures contracts are traded at exchanges around the world. As we mentioned above, the reset rate is based on the prevailing market interest rate. This market rate is usually the LIBOR or the Interbank Offer Rate in the currency's domestic financial center. In the late 1990s, Eurocurrency futures contracts included: i. ii. iii. iv. v. vi. vii. viii. ix. Eurosterling (at LIFFE, the London International Financial Futures Exchange). Euroyen (at TIFFE, the Tokyo International Financial Futures Exchange, LIFFE, and the Singapore International Monetary Exchange, SIMEX). Euroswiss Franc (at LIFFE). Eurodollar (at the CME in Chicago, LIFFE, SIMEX, and TIFFE). Euribor (at LIFFE, MATIF in Paris, MEFF, the Mercado Español de Futuros Financieros, in Barcelona, and Belfox in Brussels). Euro (LIBOR) (at LIFFE). HIBOR (at the Hong Kong Futures Exchange). JIBOR (at SAFEX, the South African Futures Exchange in Johannesburg). SIBOR (at SIMEX). We will focus on the three-month Eurodollar futures at the Chicago Mercantile Exchange in Chicago. The mechanics of the other Eurocurrency futures contracts are very similar to the mechanics of the Eurodollar futures contract. The Eurocurrency futures market provides some of the key reference rates for interbank trading in Eurocurrencies. Eurocurrency futures contracts are like any other futures contracts (see Chapter VI). If the price goes up, the long side wins and the short side loses. The Eurodollar futures price is based on three-month LIBOR, the offered interest rate for three-month Eurodollar deposits (for forward delivery) with a face value of USD 1,000,000. The interest rate on a (forward) three- month deposit is quoted at an annual rate. The Eurodollar futures price is defined to be: 100 - (the interest rate of a 3-mo Eurodollar deposit for forward delivery). Example XV.2: If the interest rate on the forward 3-mo. deposit is 6.43%, the Eurocurrency futures price is 93.57. ¶  Interest rates and Eurodollar futures: Inverse Relation If interest rates go up, the Eurodollar futures price goes down, so the short side of the futures contract makes money.  XV.2 Since the face value of the contract is USD 1,000,000, one basis point (.01%) has a value of USD 100 for a 360-day deposit. For a three-month deposit, the value of one basis point is thus logically USD 25. Example XV.3: If the futures price drops 2 bps, from 89.64 to 89.62, then the short rate side gains: 2 x USD 25 = USD 50. ¶ Eurocurrency futures reflect market expectations of forward 3-month rates. An implied forward rate (f ) indicates approximately where short-term rates may be expected to be sometime in the future. Example XV.4: 3-month LIBOR spot rate = 5.44% (91 day period) 6-month LIBOR spot rate = 5.76% (182 day period) 3-month forward rate = f (1 + .0576 * 182/360) = (1 + .0544 * 91/360) * (1 + f * 91/360)  f = [(1 + 0.0576 * 182/360)/(1 + 0.0544 * 91/360) – 1] * (360/91) f = 0.059975 (6.00%). ¶ At all exchanges Eurodollar futures are traded for delivery in March, June, September, December, plus four serial months and spot month. Delivery at the CME is hypothetically made on the third Wednesday of the month. The last day of trading is two days prior to the third Wednesday. Three-month Eurodollar contracts are traded with delivery dates as far as ten years. However, they are only liquid out to about four years. In Eurocurrencies, delivery is only "in cash." No Eurocurrency deposit is actually delivered on the CME Eurocurrency futures contract. The CME forces the Eurodollar futures price to converge to the spot price by the way the exchange determines the settlement price on the final day of trading. The CME keeps a list of at least twenty London banks that deal in Eurodollar deposits. On the last day of trading, at 3:30 PM London time and at a random time interval in the last ninety minutes of trading, they take a sample of twelve of these banks and obtain their quotations for three-month LIBOR. The arithmetic average of these two values is the final settlement price on the final day of trading. Example XV.5: The Wall Street Journal on October 24, 1994 quotes the following Eurodollar contracts: EURODOLLAR (CME) - $ 1 million; pts of 100% Yield XV.3 Open Open High Low Settle Chg Settle Chg Dec 94.00 94.03 93.97 94.00 .... 6.00 .... Mr95 93.56 93.60 93.53 93.57 + .01 6.43 - .01 June 93.11 93.15 93.07 93.12 + .01 6.88 - .01 Sept 92.77 92.80 92.73 92.77 .... 7.23 .... Dec 92.45 92.49 92.42 92.46 .... 7.54 .... Mr96 92.38 92.41 92.34 92.38 .... 7.62 .... June 92.26 92.28 92.24 92.25 - .01 7.75 + .01 Sept 92.16 92.18 92.12 92.15 - .01 7.85 + .01 Dec 92.04 92.06 92.01 92.03 - .01 7.97 + .01 Mr97 92.05 92.06 92.01 92.04 - .01 7.96 + .01 June 91.98 92.01 91.95 91.97 - .01 8.03 + .01 Sept 91.92 91.94 91.89 91.91 - .01 8.09 + .01 Dec 91.81 91.82 91.77 91.79 - .01 8.21 + .01 Mr98 91.83 91.84 91.79 91.81 - .01 8.19 + .01 June 91.77 91.78 91.73 91.75 - .01 8.25 + .01 Sept 91.71 91.73 91.67 91.69 - .01 8.31 + .01 Dec 91.60 91.61 91.56 91.58 - .01 8.42 + .01 Mr99 91.62 91.63 91.58 91.60 - .01 8.40 + .01 June 91.56 91.57 91.52 91.54 - .01 8.46 + .01 Sept 91.50 91.51 91.46 91.48 - .01 8.52 + .01 Dec 91.40 91.41 91.36 91.37 - .01 8.63 + .01 Mr00 91.44 91.44 91.40 91.41 - .01 8.59 + .01 June 91.39 91.40 91.35 91.36 - .01 8.64 + .01 Sept 91.34 91.35 91.30 91.31 - .01 8.69 + .01 Dec 91.23 91.24 91.19 91.21 .... 8.79 .... Mr01 91.28 91.28 91.24 91.26 .... 8.74 .... June 91.24 91.24 91.20 91.22 .... 8.78 .... Sept 91.21 91.20 91.17 91.19 .... 8.81 .... Dec .... .... .... 91.09 .... 8.91 .... Mr02 91.13 91.13 91.13 91.14 .... 8.86 .... June .... .... .... 91.10 .... 8.90 .... Sept 91.06 91.06 91.06 91.08 .... 8.92 .... Dec 90.97 90.97 90.97 91.00 .... 9.00 .... Mr03 91.01 91.03 91.01 91.04 .... 8.96 .... June 90.97 90.97 90.97 91.00 .... 9.00 .... Sept 90.85 90.98 90.95 90.98 .... 9.02 .... Dec 90.85 90.88 90.85 90.89 - .01 9.11 + .01 Est vol 437,328; vol Thur 615,913; open int 2,576,727. +17,451. Interest 447,913 402,624 302,119 243,103 176,045 152,827 124,984 117,214 95,555 83,127 69.593 55,103 53,103 43,738 37,785 26,751 24,137 21,890 15,989 10,263 7,354 7,536 4,971 7,691 6,897 7,312 5,582 5,040 3,845 2,689 2,704 2,016 1,341 1,589 1,367 1,354 1,227 Let's focus on the Mar 95 contract. The "open" price of 93.56 was the market-determined price at which a contract traded (someone going long, someone going short) when the market opened at the beginning of the day. The final settlement price for the day was 93.57, which was one basis points higher ("change" = +.01) than the previous day's settlement price. That is, between the close of each of the two days, the long position holders had their account balances increased by (credited with) USD 25 (1 x USD 25). The "yield" is an unnecessary column, since the 6.44% interest rate on three-month Eurodollar deposit can be obtained as 100 - 93.56 = 6.44. ¶  The LIFFE “Euro-euro” Contract: Euribor and Euro (LIBOR) Several European Futures Exchanges offer a Eurocurrency futures contract based on the Euro. The contract specifications are similar to the Eurodollar specifications. The LIFFE XV.4 offers a Eurocurrency futures based on the Euribor (the European Bankers Federation’s Interbank Offered Rate). The LIFFE also offers a Eurocurrency futures (LIBOR). The contract based on Euribor is the most liquid contract at the LIFFE. The LIFFE Euribor futures price is based on three-month Euribor, the offered interest rate for three-month Euro deposits (for forward delivery) with a face value of EUR 1,000,000. The interest rate on a (forward) three- month deposit is quoted at an annual rate. The minimum price movement is .005 and it has a value of EUR 12.50. Delivery months are March, June, September, December and two serial months. The contracts are settled in cash based on the Exchange Delivery Settlement Price. The settlement price is set to 100.00 minus the Euribor. The MATIF, the MEF, and the Belfox also offer a Eurocurrency futures contract based on Euribor.  1.A Some Terminology Several factors must always be kept in mind when hedging with Eurodollar or other interest-rate futures. Amount: A Eurodollar futures contract involves a face amount of USD 1 million. To hedge USD 7 million borrowing for three months, we would need seven futures contracts. Duration: Duration measures the time at which cash flows take place. For money market instruments, all cash flows generally take place at the maturity of the instrument. A sixmonth deposit has approximately twice the duration of a three-month deposit. Therefore, the value of one basis point for six months is approximately USD 50. One could hedge a USD 1 million six-month deposit beginning in March, with two March Eurodollar futures (stack hedge). One could also hedge it with one March Eurodollar future and one June Eurodollar future (strip hedge). Slope: Eurodollar contracts may be used to hedge other interest rate assets and liabilities, such as T-bills, commercial paper, banker's acceptances, etc. The rates on these instruments may not be expected to change one-for-one with Eurodollar interest rates. If we define f as the interest rate in a Eurodollar futures contract, then slope =  underlying interest rate / f. If the rate of change of T-bill rates with respect to Eurodollar rates is .9 (slope = .9), then we would only need nine Eurodollar futures contracts to hedge USD 10 million of threemonth T-bill. Let FA and DA be the face amount and duration of the underlying asset to be hedged. Then the number n of Eurodollar futures needed to hedge is n = (FA/1,000,000) x (DA/90) x slope. XV.5 Example XV.6: To hedge USD 10 million of 270-day commercial paper with a slope of .935 would require approximately twenty-eight contracts. ¶ Margin: Eurodollar futures require a deposit of initial margin. In September, this was typically USD 800 per contract, while maintenance margin was USD 600. 1.B The Eurostrip Yield Curve and the CME Swap Successive Eurocurrency futures give rise to a strip yield curve. The March future involves a three-month rate of interest that begins in March and ends in June. The June future involves a three-month rate of interest that begins in June and ends in September and so on. There are some holes in the curve so defined: between the third Wednesday of March and the third Wednesday of June there will be 91 or 98 days (multiples of 7). But the Eurocurrency futures only cover 90 of these days. For example, one Eurodollar future does not quite hedge USD 1 million for the complete three months. The approximation, however, is close. This strip yield curve is called Eurostrip. If we compound the interest rates for four successive Eurocurrency contracts, we define a one-year rate composed from the four three-month rates. Obviously, the one-year rate so constructed cannot differ much from the implied forward rate for the same period, for example, as calculated from the yield curve. Example XV.7: Replicating a zero-coupon bond with a Eurodollar strip. Suppose Mr. Peterson, a money manager, expects to receive USD 2,000,000 on the date that the December 95 Eurodollar futures expires. He wants to invest the money in the Eurodollar market. He is concerned that interest rates may fall during the next three months. Mr. Peterson uses the long Eurodollar strip to hedge against the interest rate uncertainty. Today, October 24, 1994, the December, March, June and September futures are trading at 94.00, 93.57, 93.12 and 92.77, respectively -see Example XV.5. The December-March interest rate con be fixed today on the forthcoming USD 2,000,000 by purchasing two December Eurodollar futures. The rate is fixed at 6% annually, or 1.5% for the December-March period. If in December 1994 the 3-mo Eurodollar rate falls to 4%, then a 1% rate of return would earn over the December-March period on the USD 2,000,000 spot investment, that is, USD 20,000. But to this spot return we should add the return on the December Eurodollar contract, which is 200 bps x USD 25 = USD 5,000 per contract. Then, the effective return is USD 20,000 + USD 10,000 = USD 30,000 (or 1.5%). Therefore, in March 1995, the spot three-month investment will have accrued to USD 2,030,000. The 6.43% annual rate, or 1.6075% quarterly rate, for the March-June interval can be locked in today on that amount by purchasing 2 x 1.015 March Eurodollar contracts. The total return for this second 3-mo. period amounts to USD 32,632.25 (USD 203,000,000 x .016075). The total amount accrued by the end of the March-June period contract is: XV.6 USD 2,000,000 x 1.015 x 1.016075 = USD 2,062,632.30. Extending the above reasoning, to lock in a reinvestment rate today for the June-September interval on the resulting USD 2,062,632.30, Mr. Peterson needs to buy 2 x 1.05 x 1.01675 June contracts today. This purchase locks in a 1.72% (6.88/4) quarterly rate on that balance. And to fix the final September-December's reinvestment rate at 1.8325% on the September balance of USD 2,000,000 x 1.015 x 1.016075 x 1.0172, Mr. Peterson needs to buy 2 x 1.015 x 1.016075 x 1.0172 September futures today. Mr. Peterson has fixed a one-year investment today at the rate of (1.015 x 1.016075 x 1.0172 x 1.018325) - 1 = .0682787 (or 6.82787%). We should note that since all the proceeds are reinvested, Mr. Peterson receives the proceeds in a year at the end of the September contract. Thus, buying the one-year Eurostrip is equivalent to buying a one-year zero-coupon bond. ¶ A CME swap involves a trade whereby one party receives one-year fixed interest and makes floating payments of the three-month LIBOR. The payments dates in a CME swap correspond to Eurodollar futures expiration dates. Example XV.8: On August 15, one might do a September-September swap. The floating-rate payer would make payments on the third Wednesday in December, as well as on the third Wednesday of the following March, June, and September. The fixed-rate payer would make a single payment on the last of these dates.¶  CME swaps and the Eurostrip: Arbitrage works Because the floating payment dates correspond to CME settlement dates, arbitrage ensures that the one-year fixed rate of interest in the CME swap does not diverge materially from the one-year rate constructed from the Eurostrip.  1.B.1 Pricing Short-Dated Swaps The swap coupons for short-dated fixed-for-floating interest rate swaps are routinely priced off the Eurostrip. The key to pricing the swap coupon is to equate the present values of the fixed-rate side and the floating-rate side of the swap. Eurocurrency futures contracts provide a way to do that. The estimation of the fair mid-rate is complicated by the fact that (a) the convention is to quote swap coupons for generic swaps on a semiannual bond basis, and (b) the floating side, if pegged to LIBOR, is usually quoted on a money market basis (for consistency, we will assume that the swap coupon is on quoted a bond basis). For purposes of notation, if the swap is to have a tenor of m months (m/12 years) and is to be priced off three-month Eurodollar futures, then pricing will require n sequential futures series, where n=m/3 or equivalently, m=3n. XV.7 The procedure by which the dealer obtains an unbiased mid-rate for pricing the swap coupon involves three steps: i. Calculate the implied effective annual LIBOR for the full duration (full-tenor) of the swap from the Eurostrip. r0,3n = t=1n [1 + r3(t-1),3t A(t)/360] - 1,  = 360/tA(t) A(t) is the number of days covered by the Eurodollar futures contract that starts at time t. ii. Convert the full-tenor LIBOR, which is quoted on money market basis, to its fixedrate equivalent FRE0,3n, which is stated as an effective annual rate (annual bond basis). FRE0,3n = r0,3n x (365/360). iii. Restate the fixed-rate equivalent on the same payment frequency as the floating side of the swap. The result is the swap coupon SC. This adjustment is given by k=frequency of payments. SC = [(1 + FRE0,3n)1/k - 1] x k, Example XV.9: On October 24, 1994, Housemann Bank, a swap dealer, wants to price a one-year fixed-for-floating interest rate swap against 3-month LIBOR, that starts on December 94. The fixed rate will be paid quarterly and, therefore, is quoted quarterly bond basis. Housemann Bank wants to find the fixed rate that has the same present value (in an expected value sense) as four successive 3mo. LIBOR payments. In Table XV.A, we summarize the Eurostrip for the first five contracts from Example XV.5. Dec 94 Mar 95 Jun 95 Sep 95 Dec 95 Price 94.00 93.57 93.12 92.77 92.46 TABLE XV.A Eurodollar Futures, Settlement Prices (October 24, 1994) Implied Number of 3-mo. LIBOR Notation Days Covered 6.00 0x3 90 6.43 3x6 92 6.88 6x9 92 7.23 9 x 12 91 7.56 12 x 15 91 First, Housemann Bank calculates the implied LIBOR rate corresponding to the full-tenor of the swap using (i). Since the swap is for twelve months, n=4. The implied one-year LIBOR is: f0,12 = [(1+.06x(90/360)) x (1+.0643x(92/360)) x (1+.0688x(92/360)) x (1+.0723x(91/360))]360/365- 1 = .06760814 (money market basis). Second, Housemann Banks converts this money market rate to its effective equivalent stated on an annual bond basis. FRE0,12 = .06760814 x (365/360) = .068547144. XV.8 Third, since the coupon payments are quarterly, k=4, Housemann Bank must restate this effective annual rate on an equivalent quarterly bond basis. SC = [(1.068547144)1/4 - 1] x 4 = .0668524 (quarterly bond basis) Therefore the swap coupon mid-rate is 6.68524%. ¶ Example XV.10: Go back to Example XV.9. Suppose now, that Housemann Bank, instead of pricing a one-year swap with quarterly fixed-rate payments against 3-month LIBOR, wants to price a one-year swap with semiannual fixed-rate payments against 6-month LIBOR. The swap coupon mid-rate is calculated to be: SC = [(1.068547144)1/2 - 1] x 2 = .06741108 (semiannual bond basis). ¶ The simple procedure described above allows a dealer to quote swaps having tenors out to the limit of the liquidity of Eurodollar futures on any payment frequency desired and to fully hedge those swaps in the Eurostrip. The latter is accomplished by purchasing the components of the Eurostrip to hedge a dealer-pays-fixed-rate swap or selling the components of the Eurostrip to hedge a dealer-pays-floating-rate swap. 1.C Gap Risk Management Now, consider the use of Eurocurrency futures to hedge gap risk. Gap risk arises in Eurobanking when assets and liabilities have different maturities. Such gaps tend to be managed with futures, forward rate agreements (FRA), and interest rate swaps because these use less capital than do time deposits. Example XV.11: It is March 20. A Swiss bank is quoted a rate of 4% on three-month Euribor deposits in the interbank market. If a EUR 2,000,000 deposit is borrowed today, the value date will be March 24. Thus, the deposit will mature on June 24 (91 days). Today, the bank can lend a sixmonth Euribor deposit at 4 1/4%, with a value date on March 24 and maturity date on September 24 (183 days). The Swiss bank receives a three-month deposit, but makes a six-month loan. Therefore, the Swiss bank is exposed to gap risk. The Swiss bank is uncertain over the interbank deposit interest rate on August 24: the implied interest rate for June 24, f, might be quite different than the actual rate on June 24. In these cases, the Swiss bank follows a very simple rule: the bank will take the three-month deposit only if it is possible to hedge the risk and make a profit. The bank decides to manage this gap risk using June Euribor futures. LIFFE lists a very active Euro (Euribor) contract. The characteristics of this contract are the same as the CME's Eurodollar contract. In particular, the face value is EUR 1,000,000. On March 20, June Euribor futures are trading at 96.13. Taken together, these prices imply the bank can lend a sixmonth deposit, funding this loan by a sequence of two three-month deposits, and be assured of a profit for the six months. XV.9 The situation of the bank is straightforward. If the bank lends for six months, it will receive interest at 4 1/4%. But for the first three months it will only pay interest on its borrowed three-month deposit at 4%. The bank should calculate the implied rate to see if a profit can be locked in on the three-month deposit. The Swiss bank calculates the implied forward rate, f, as the rate the bank can afford to pay on the second three-month deposit and still break even: [1 + .0425x(183/360)] = [1 + .04x(91/360)]x[1 + f x (92/360)]  f = 4.452%. If the Swiss bank can be certain that it will pay a rate less than 4.452% for the second three-month period, the bank will make a profit. June Euribor is trading at 3.87%. Then, by going short two June contract at 96.13 (3.87%) the Swiss bank locks in a profit. ¶ II. Forward Rate Agreements (FRA) A forward rate agreement (FRA) is cash-settled forward contracts on interest rates traded among major international banks active in the Eurodollar market. You can think of an FRA as the OTC equivalent of a Eurodollar futures contract. Banks use FRAs to fix interest costs on anticipated future deposits or interest revenues on variable-rate loans. A bank that sells an FRA agrees to pay the buyer the increased interest cost on some notional principal amount if interest rates rise above the agreed (“forward”) rate on the contrat maturity or settlement rate. On the other hand, the buyer agrees to pay the seller the increased interest cost if interest rates fall below the forward rate. Example XV.12: An FRA on a three-month interest rate for a three-month period beginning six months from the present and terminating nine months from the present. This agreement is called a "six against nine" (6x9) FRA because it fixes the interest rate for a deposit to be placed after three months and maturing nine months from today. The contract would be settled in cash in six month – i.e., at the beginning of the FRA period. 3 months Today 6 months 9 months Cash settlement Let f be the forward rate (expressed as a decimal); i, the settlement rate; N, the nominal contract amount; ym, the number of days in the FRA period; and yb, the year basis (360 or 365). Thus, if i > f, the seller pays the buyer: N x (i-f) x (ym/yb) 1 + i x (ym/yb) XV.10