[PDF] CALCULATING EURO SWAPNOTE® FUTURES PRICES





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  • What is bootstrapping zero coupon rates?

    What is Bootstrapping Yield Curve? Bootstrapping is a method to construct a zero-coupon yield curve. The slope of the yield curve provides an estimate of expected interest rate fluctuations in the future and the level of economic activity.

  • How to bootstrap zero rates?

    Bootstrapping Spot Rate Curve (Zero Curve)

    1Step 1: Decide on the Instrument for Yield Curve. 2Step 2: Select the Par Yield Curve. 3Step 3: Interpolate the Missing Yields. 4Step 4: Calculate Spot Rates Using Treasury Yields.

  • What is bootstrapping formula?

    Example: Bootstrapping Spot Rates
    The one-year implied spot rate is 2%, as it is simply the one-year par yield. The two-year implied spot rate is determined as follows: 1=0.0261.02+(1+0.026)(1+r(2))2r(2)=2.61%
  • To calculate the yield-to-maturity (YTM) on a zero-coupon bond, first divide the face value (FV) of the bond by the present value (PV). The result is then raised to the power of one divided by the number of compounding periods.
CALCULATING EURO SWAPNOTE® FUTURES PRICES

INTEREST RATE DERIVATIVES

Euro Swapnote

futures are priced like a notional bond futures contract. The notional underlying bond has an annual coupon of

6% falling on each anniversary of the contract's reference day

("effective date"), based on a notional underlying of €100,000. Euro

Swapnote

futures are quoted per €100 nominal.

Euro Swapnote

EDSP (The Exchange Delivery Settlement Price)

Euro Swapnote

futures contracts are cash settled on the last trading day against a single price set by the Exchange (the EDSP). The EDSP is calculated as sum of the present values on the effective date of all of the cash flows in the notional underlying bond. Each cashflow will fall on the anniversary of the notional delivery date, and based upon a coupon rate of 6% per annum is equivalent to €6 per €100 nominal. The present value of each cashflow is discounted using a zero coupon curve derived from euro par swap market rates published by ISDA two days prior to the effective date. Coupon payment dates are determined using the Modified Following Business Day Convention, i.e. if an anniversary date falls on a non-working day, the coupon payment date is moved to the next working day. Consequently the coupon payment amount is adjusted using the Relevant Daycount Fraction "Ai " in accordance with a 30/360 day count basis. Example: The EDSP for the June 2012 5 Year € Swapnote futures contract

Effective Date: 20 June 2012TERM (YEARS)CASHFLOW

DATEDAYCOUNT (A

i )ISDAFIX

® (R

i )ZERO COUPON

DISCOUNT

FACTOR (D

i )CASHFLOW

DISCOUNTED

CASHFLOW

120 Jun 131.000000000.559%0.994441076.000000005.96664642

220 Jun 141.000000000.845%0.983288196.000000005.89972914

322 Jun 151.005555560.933%0.972424666.033333365.866962141

420 Jun 160.994444441.086%0.957561325.966666645.713449184

520 Jun 171.000000001.252%0.93931416106.0000000099.56730096

EDSP123.01

CALCULATING EURO SWAPNOTE

FUTURES PRICES

Fast Facts

What is it?

Euro Swapnote®

is an on-exchange futures contract referenced to the European interbank curve.

Who is it for?

Euro Swapnote

futures are for anyone who wishes to gain or hedge exposure to the

European interest rate swaps curve via a

centrally cleared contract.

What does it provide?

Euro Swapnote

provides an open and efficient means of gaining euro swap market exposure in a contract that already meets new regulatory requirements.

Bootstrapping Technique

To calculate the zero coupon discount factors using the swap market rates, the following "bootstrapping" technique is employed. The one year swap rate represents a single fixed payment, with the first discount factor calculated as follows: d i =1 1 + A i R i

Where R

i is the one year euro swap rate quoted vs. 3 month Euribor in nominal terms. As per the example, R i =0.00599. The swap rates for two years and beyond cover multiple annual fixed payments. The bootstrapping methodology needs to take into account earlier annual payments to calculate the zero discount factor for each subsequent payment; calculated as follows: d i =1 - R i ∑ A j d j 1 + A i R i

Euro Swapnote

Market Price

The market price of Swapnote

futures can be calculated using forward par swap rates as of the contract's effective date. Euro Swapnote futures effective dates follow the IMM convention, i.e. Swapnote futures can be calculated using IMM par swap rates. Euro par swap rates represent the annual fixed rates payable on a fixed-for- floating interest rate swap of different term-to-maturities. Euro par swap rates are established on the basis that the value of a par swap at the start of the swap's life is zero. To have the starting value equal to zero, the fixed rate on the swap has to be set such that the present value of the swap's fixed payments equals the present value of the swap's floating payment. The IMM par swap rates can be calculated using a forwarding curve with future payments present valued using a discounting curve as follows:

For a par swap:P V fixed = P V floating

P V fixed = fixedrate x ∑ daycount n x discount n P V floating = ∑ floatrate m x daycount m x discount m

Re-arranging:fixedrate =∑ floatrate

m x daycount m x discount m ∑ daycount n x discount n i - 1 j = 1 Example: 2 Year IMM par swap rate quoted vs. 6 month Euribor

Valuation Date:

12 June 2012

IMM Date:

20 June 2012

FIXED SIDEFLOATING SIDE

PAYMENT DATEDAYCOUNTEONIA DISCOUNT

(DISCOUNTING

CURVE)6M EURIBOR

(FORWARDING

CURVE)DAYCOUNTEONIA DISCOUNT

(DISCOUNTING

CURVE)

20 Dec 120.937%0.500000000.99862

20 Jun 131.000000000.997420.821%0.500000000.99742

20 Dec 130.836%0.500000000.99600

20 Jun 141.000000000.994000.938%0.500000000.99400

SUM1.991420.017598

FIXED RATE= 0.017598 / 1.99142 = 0.884% (to 3 d.p.) Using this technique, IMM par swap rates can be calculated for all relevant cashflows in the 2, 5 and 10 Year € Swapnote contracts.

2 YEAR € SWAPNOTE

MATURITYANNIVERSARY

DATE (IMM)IMM PAR SWAP

RATEDAYCOUNTZERO COUPON

DISCOUNT

FACTORCASHFLOWDISCOUNTED

CASHFLOW

120 Jun 130.607%1.000000000.993962766.000000005.96377656

220 Jun 140.884%1.000000000.98253670106.00000000104.14889020

VALUE110.115

5 YEAR € SWAPNOTE

MATURITYANNIVERSARY

DATE (IMM)IMM PAR SWAP

RATEDAYCOUNTZERO COUPON

DISCOUNT

FACTORCASHFLOWDISCOUNTED

CASHFLOW

120 Jun 130.607%1.000000000.993962766.000000005.96377656

220 Jun 140.884%1.000000000.982536706.000000005.89522020

322 Jun 150.985%1.005555560.970908946.033333365.85781730

420 Jun 161.133%0.994444440.955773735.966666645.70278323

520 Jun 171.293%1.000000000.93742789106.0000000099.36735634

VALUE122.79

10 YEAR € SWAPNOTE

MATURITYANNIVERSARY

DATE (IMM)IMM PAR SWAP

RATEDAYCOUNTZERO COUPON

DISCOUNT

FACTORCASHFLOWDISCOUNTED

CASHFLOW

120 Jun 130.607%1.000000000.993962766.000000005.96377656

220 Jun 140.884%1.000000000.982536706.000000005.89522020

322 Jun 150.985%1.005555560.970908946.033333365.85781730

420 Jun 161.133%0.994444440.955773735.966666645.70278323

520 Jun 171.293%1.000000000.937427896.000000005.62456734

620 Jun 181.436%1.000000000.917301496.000000005.50380894

720 Jun 191.557%1.000000000.896387786.000000005.37832668

822 Jun 201.663%1.005555560.874744386.033333365.27762445

921 Jun 211.752%0.997222220.853137295.983333325.10460477

1020 Jun 221.833%0.997222220.83107561105.9833333288.08016339

VALUE122.79

Further Information

Interest Rate Derivatives

+44 (0)20 7429 4640
rates@theice.com theice.com/products/futures-&- options/financials/interest-rates

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