Replicating Interest Rate Swaps with Eurodollar Strips - MemoFin.fr

Replicating Interest Rate Swaps with Eurodollar Strips - MemoFin.fr Replicating Interest Rate Swaps with Eurodollar Strips - MemoFin.fr

10.07.2015 Views

eceiver) is generally referred to simply as the“payer” while the fixed rate receiver (floating ratepayer) may be referred to simply as the “receiver.”Interest Rate Swap (IRS)For example, one may swap a quarterly paymentbased upon a specified fixed rate of interest, such as1%, applied to a principal value of $10 million forthe next 5 years; for a quarterly payment basedupon 3-month LIBOR rates applied to a principalvalue of $10 million for the next 5 years. Theseperiodic fixed vs. floating rate payments are typicallynetted such that only the net amount due is passedbetween payer and receiver.Clearly, the fixed rate payer hopes that floatingrates rise such that his future receipts are increased.The floating rate payer, or fixed rate receiver, hopesthat floating rates decline such that his futurepayments are diminished.ED Volume (Mill Cnts)FixedRatePayer1,0009008007006005004003002001000FixedPaymentsFloatingPaymentsEurodollar & IRS Growth1981198319851987198919911993199519971999200120032005200720092011EurodollarsDealerFixedPaymentsFloatingPaymentsIRSFixedRateReceiver$450$400$350$300$250$200$150$100$50The seminal interest rate swap transaction wasconcluded in 1980 while Eurodollar futures wereoriginally introduced in 1981. Since that time the$0Outstanding IRS (Trillions)IRS market has grown to some $379.4 trillion inoutstanding notional value as of June 2012. 1Volume in CME Eurodollar products have grown on astrikingly parallel path along with over-the-counterswaps. This underscores the fact that Eurodollarfutures and inextricably intertwined with the IRSmarket as a source for pricing and a tool to hedgethe risks associated with swaps. In particular, banksand broker-dealers making a market in over-thecounter(OTC) swaps represent primary Eurodollarmarket participants.BBA LIBOR SwapThe British Banker’s Association (BBA) LIBOR fixingsrepresent a benchmark against which many interestrate products including CME Eurodollar futures andinterest rate swaps routinely are pegged. Becauseof this focus on the BBA LIBOR fixing rate and theliquidity associated with Eurodollar futures, aparticular type of IRS – a “BBA LIBOR Swap” – isfrequently traded in the over-the-counter (OTC)markets.A BBA LIBOR Swap may be constructed to referencethe 3-month BBA LIBOR fixing as the basis for thefloating rate payments, frequently on the samedates as standard CME Eurodollar futures are settled(so-called “IMM dates”).As such, there is a closely compatible relationshipbetween BBA LIBOR Swaps and CME Eurodollarfutures that facilitates use of futures as a referencefor pricing, and a tool for hedging, swaps. Further,this implies that futures may be used as a proxy tomimic the performance of a BBA LIBOR Swap, albeitwith some qualifications. 21 As reported by the Bank of International Settlements(BIS) in its semi-annual survey of the over-the-counter(OTC) derivatives marketplace.2 Note that, unlike OTC swaps, CME Eurodollar futures donot exhibit convexity, or a non-linear relationshipbetween price and yield. Rather, futures exhibit a linearrelationship such that a one basis point (0.01%) changein yield uniformly represents a monetary change of$25.00 in the value of a single futures contract. Thislack of convexity implies that one must adjust one’sEurodollar position periodically in order to achieve asimilar effect.3 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

Pricing SwapsInterest rate swaps are typically quoted (on anopening basis) by reference to the fixed rate ofinterest. That fixed rate is calculated as the ratethat renders equivalent the present value of theanticipated periodic fixed rate payments (PV fixed );with the present value of the anticipated periodicfloating rate payments (PV floating ).Those floating rate payments may be estimated byexamining the shape of the yield curve, or morepractically, by referencing the rates associated withEurodollar futures prices which reflect the shape ofthe curve.PV Fixed = PV FloatingWhen an IRS is transacted such that the presentvalue of the estimated floating rate payments equalsthe present value of the fixed rate payments, nomonetary consideration is passed on the basis ofthis initial transaction. This is also referred to as a“par swap.” In other words, the “non-par payment”(NPP) is set at zero ($0).NPP = 0 = PV Floating − PV FixedThe fixed rate (R fixed ) associated with a swap may becalculated by reference to the following formula.R fixed = 4 ∙ ∑ni=1PV i ∙ R i ∙ days i∑ni=1PV i360 Where PV i = present value discounting factor; R i =rate associated with each successively deferredperiod; days i = number of days in each successivelydeferred period. Note that those rates may bedetermined by reference to Eurodollar futurespricing.For example, find the value of a 2-year swap wherethe floating rate is estimated by reference to theBBA 3-month Eurodollar time deposit rate as ofJanuary 30, 2013. Table 4, found in the appendixbelow, provides details regarding the calculations.The fixed rate of interest associated with the swapmay be calculated as 0.3861%.The present value of the fixed and floating ratepayments given a fixed rate of 0.3861% may becalculated as $76,934.49. The equivalence of thesetwo cash flow streams may be established byreference to Table 5 found in the appendix. As such,this is a par swap that may be transacted with noup-front monetary consideration.R fixed = 4 ∙ 0.9997 ∙ 0.002265 ∙ 47360 + 0.9989 ∙ 0.003000 ∙ 91360 + 0.9981 ∙ 0.003300 ∙ 91360 + 0.9972 ∙ 0.003650 ∙ 91360 + 0.9962 ∙ 0.004050 ∙ 91360 + 0.9950 ∙ 0.004500 ∙ 91360 + 0.9938 ∙ 0.005100 ∙ 91360 + 0.9923 ∙ 0.005800 ∙ 91360 ÷ (0.9997 + 0.9989 + 0.9981 + 0.9972+ 0.9962 + 0.9950 + 0.9938 + 0.9923)= 0.3861%Note that, once transacted, an IRS might be ratherunique to the extent that there are a plethora ofvariables associated with the transaction. Theseinclude features such as the specific floatingreference rate, the periodic reset dates, the dateconventions, etc. Because there are a large numberof variable features associated with an IRS, themarket for swaps is fragmented amongst manyoutstanding swaps with divergent contract termsand conditions.Because the swap market is rather fragmented, bilateralcounterparties who wish to close or retire anoutstanding swap transaction frequently mustnegotiate such a “close-out” or “tear-up” directlywith the original counterparty. These closingtransactions are typically quoted by reference to thenon-par value of the swap at the time of such closeout.For example, interest rates may have advancedsince the original transaction was concluded at aNPP=0. As such, the fixed rate payer is advantagedwhile the floating rate payer is disadvantaged.Thus, the floating rate payer may be required tocompensate the fixed rate payer with a NPP thatreflects the difference between the PV floating andPV fixed per current market conditions.4 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

eceiver) is generally referred to simply as the“payer” while the fixed rate receiver (floating ratepayer) may be referred to simply as the “receiver.”<strong>Interest</strong> <strong>Rate</strong> Swap (IRS)For example, one may swap a quarterly paymentbased upon a specified fixed rate of interest, such as1%, applied to a principal value of $10 million forthe next 5 years; for a quarterly payment basedupon 3-month LIBOR rates applied to a principalvalue of $10 million for the next 5 years. Theseperiodic fixed vs. floating rate payments are typicallynetted such that only the net amount due is passedbetween payer and receiver.Clearly, the fixed rate payer hopes that floatingrates rise such that his future receipts are increased.The floating rate payer, or fixed rate receiver, hopesthat floating rates decline such that his futurepayments are diminished.ED Volume (Mill Cnts)Fixed<strong>Rate</strong>Payer1,0009008007006005004003002001000FixedPaymentsFloatingPayments<strong>Eurodollar</strong> & IRS Growth1981198319851987198919911993199519971999200120032005200720092011<strong>Eurodollar</strong>sDealerFixedPaymentsFloatingPaymentsIRSFixed<strong>Rate</strong>Receiver$450$400$350$300$250$200$150$100$50The seminal interest rate swap transaction wasconcluded in 1980 while <strong>Eurodollar</strong> futures wereoriginally introduced in 1981. Since that time the$0Outstanding IRS (Trillions)IRS market has grown to some $379.4 trillion inoutstanding notional value as of June 2012. 1Volume in CME <strong>Eurodollar</strong> products have grown on astrikingly parallel path along <strong>with</strong> over-the-counterswaps. This underscores the fact that <strong>Eurodollar</strong>futures and inextricably intertwined <strong>with</strong> the IRSmarket as a source for pricing and a tool to hedgethe risks associated <strong>with</strong> swaps. In particular, banksand broker-dealers making a market in over-thecounter(OTC) swaps represent primary <strong>Eurodollar</strong>market participants.BBA LIBOR SwapThe British Banker’s Association (BBA) LIBOR fixingsrepresent a benchmark against which many interestrate products including CME <strong>Eurodollar</strong> futures andinterest rate swaps routinely are pegged. Becauseof this focus on the BBA LIBOR fixing rate and theliquidity associated <strong>with</strong> <strong>Eurodollar</strong> futures, aparticular type of IRS – a “BBA LIBOR Swap” – is<strong>fr</strong>equently traded in the over-the-counter (OTC)markets.A BBA LIBOR Swap may be constructed to referencethe 3-month BBA LIBOR fixing as the basis for thefloating rate payments, <strong>fr</strong>equently on the samedates as standard CME <strong>Eurodollar</strong> futures are settled(so-called “IMM dates”).As such, there is a closely compatible relationshipbetween BBA LIBOR <strong>Swaps</strong> and CME <strong>Eurodollar</strong>futures that facilitates use of futures as a referencefor pricing, and a tool for hedging, swaps. Further,this implies that futures may be used as a proxy tomimic the performance of a BBA LIBOR Swap, albeit<strong>with</strong> some qualifications. 21 As reported by the Bank of International Settlements(BIS) in its semi-annual survey of the over-the-counter(OTC) derivatives marketplace.2 Note that, unlike OTC swaps, CME <strong>Eurodollar</strong> futures donot exhibit convexity, or a non-linear relationshipbetween price and yield. Rather, futures exhibit a linearrelationship such that a one basis point (0.01%) changein yield uniformly represents a monetary change of$25.00 in the value of a single futures contract. Thislack of convexity implies that one must adjust one’s<strong>Eurodollar</strong> position periodically in order to achieve asimilar effect.3 <strong>Replicating</strong> IRS <strong>with</strong> <strong>Eurodollar</strong> <strong>Strips</strong> | May 16, 2013 | © CME GROUP

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