07 interest rates swaps

8/12/2019 07 Interest Rates Swaps

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April 3, [email protected]

Interest Rate Swaps


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a derivative, where two counterparties exchangeone stream of cash flows against another stream

(legs of the swap)

cash flows are calculated over a notional principalamount

over-the-counter (OTC) products

termination (cancellation) or assignment (sale to a

third party)

Swaps


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A 3-year swap initiated on March 5, 2007 betweenMicrosoft and Intel Microsoft agrees to pay an interest rate of 5% on a

principal of $100 million Intel in return agrees to pay Microsoft the 6-month LIBORrate on the same principal

Payments are to be exchanged every 6 months

Example of a plain vanilla swap*

* Example taken from Options, Futures and Other Derivatives by J.Hull, p.148.

MicrosoftFixed-rate payer

IntelFloating-rate payer

LIBOR5%


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There are 6 exchanges of payments on the swap:

1st exchange of payments: No uncertainty determined by the LIBOR rate at the time of the issuance ofthe contract (Mar 5, 2007)

Assume 6m LIBOR rate is 4.2% on Mar 5, 2007 Microsoft pays $2.5 million to Intel Intel pays 0.5 * 0.042 * 100 = $2.1 million to Microsoft

2nd exchange of payments: Takes place a year after the initiation of the contract

Assume 6m LIBOR rate is 4.8% on Sep 5, 2007 Microsoft pays $2.5 million to Intel Intel pays 0.5 * 0.048 * 100 = $2.4 million to Microsoft

Not all payments are settled in reality Only the difference between the two payments is exchanged

1st exchange of payments: Microsoft pays $0.4 million to Intel 2nd exchange of payments: Microsoft pays $0.1 million to Intel

Example of a plain vanilla swap contd

Microsoft

Fixed-rate payer

Intel

Floating-rate payerLIBOR

5%

Mar 5, 2007 Sep 5, 2007 Mar 5, 2008 March 5, 2010

1st payment 2nd payment 4th payment 5th payment 6th paymentContract Initiation 3rd payment


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Assume Microsoft has a floating rate loan of $ 100million at LIBOR + 10 b.p. and it entered into the

swap with Intel.

1.It pays LIBOR + 0,1% to the lender.2.It receives LIBOR from Intel.

3. It pays 5% to Intel.

Microsoft transformed the borrowings ata floating rate of LIBOR + 0.1% into

borrowings at a fixed rate of 5.1%

Swaps used to transform liability


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Swaps can be used to transform asset that earns anasset into an asset earning a floating rate Assume Microsoft owns $ 100 million in bonds that

provide an interest of 4.7% over the next 3 years andenterst into the swap with Intel.

1.It receives 4.7% on the asset.

2.It receives LIBOR from Intel.

3. It pays 5% to Intel.

Microsoft transformed the asset earning 4.7%into an asset earning LIBOR 0.3%.

Swaps used to transform an asset


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Intermediates the transacion between the twocounterparties Enters into two ofsetting swap positions

They offer terms for both fixed-rate and floating

rate payers and earn a spread for their services compensation for credit risk takeover Usually around 3-4 b.p.

Market makers for swaps

Enter into the swap positions even if they do not have anofsetting positions (called warehousing swaps) Market makers must hedge their risk by using bonds,

interest rate futures, forward rate agreements, etc.

Financial intermediary


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Swap can be characterized as a combination of a fixed-ratebond PV(fix) and a floating-rate bond PV(float)

The swap is worth zero at the initiation, thus

PV(fix) = PV(float) After the initiation, it may gain some value.

In general:

Floating-rate payer: V(swap) = PV(fix) = PV(float) Long position in fixed rate bond Short position in floating rate bond

Vice versa for the fixed-rate payer

Valuation of interest rate swaps


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For the Swap valuation assume the following:1. Spot interest for a zero coupon bond: r(0,t)

2. Implied Forward interest rate: f(t1,t2)

We have a hypothetical 3-yrs swap, floating rate = 1-year LIBORwith yearly settlement and notional of $100.

What is the fair fixed rate?

Swap valuation at the Origination - Example

r(0,1) r(0,2) r(0,3)

5% 6% 7.5%

f(0,1) f(1,2) f(2,3)

5% 7.01% 10.56%


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I. Fair fixed rate Assume (for convenience) that notional is exchanged1. Calculate the expected floating rate cash flows:

CF1 = 0.05 * 100 = 5 CF2 = 0.0701 * 100 = 7.01 CF3 = 0.1056 * 100 = 10.56 CF3 = 100

2. Use the appropriate discount rate

The value of the floating rate side equals the notional.WHY and WHEN?

Swap valuation Assigning the fair fixed rate

f(0,1) f(1,2) f(2,3)5% 7.01% 10.56%

100)075.1(

100

)075.1(

564.10

)06.1(

01.7

05.1

5332


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The fixed rate payments must satisfy:

If the interest rate changes the value of the swaps changes.

Swap valuation Assigning the fair fixed rate

7.367A

19.5042.6473A

80.496100(1.075)

1

(1.06)

1

(1.05)

1A

100(1.075)

100

(1.075)

A

(1.06)

A

(1.05)

A

32

332


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If prices or rates subsequently change, the value ofthe swap will change. It will become an asset (+ value) for one party, and a

liability (- value) for the other (the party who coulddefault).

But, the valuation method (compute the PV of thecontracted fixed cash flows and of the expectedvariable cash flows) remains the same. Based on V(swap) = PV(fix) = PV(float)

Swap valuation after Origination


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future cash flows of the floating leg given by impliedforward swap rates future cash flows of both fixed andfloating legs

discounted by zero (spot) swap rates of respective timesto maturity:

Handouts: 04_Swaps.pdf page 16

Swap valuation using swap zero curve


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Derived from swap zero curve No-arbitrage condition

zt. zero (spot) rate for time to maturity t

zt+p. zero (spot) rate for time to maturity t+ptft+p... forward rate forp years period beginning in t

years time

Implied forward yield curve


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Exercises


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(a) Calculate the dealers position for each payment in eachyear,Fill in the table below.

(b) Is the dealer fixed-receiver or fixed-payer?

(c) What kind of risk is the dealer exposed to? How can these risks be

mitigated? Explain the concept of warehousing.

Problem 1 contd

Year LIBOR rate Observed (%) Swap A Swap B Swap C Dealers Net Position

1 3.2

2 2.9

3 3.6

4 3.0

5 3.2


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Companies A and B both plan to borrow 15m for 7-years. Thecompanies face differing borrowing costs. Company A canborrow for a fixed rate of 9% per annum or a floating rate ofLIBOR+100 b.p. per annum. Company B can borrow for a fixedrate of 11% per annum or a floating rate of LIBOR+120b.p. per

annum.

(a) Under what conditions would companies A and B find aninterest rate swap beneficial?

(b) Suppose that the necessary conditions hold and that you

are employed by a financial intermediary to arrangeinterest rate swaps.

(c) Propose a swap agreement which would benefit bothcompanies and the intermediary.

Problem 2


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Assume a 1-year swap that exchanges fixed rate (semiannualcompounding) with 6M LIBOR over the notional of 200 000,where swap term structure is given as:

Half year later, swap zero curve has the following form:

Calculate the NPV of the swap.

Who is exposed to credit risk, buyer or seller of the swap?

Can one expect any movements of cash flows and NPV?

Problem 4

3M 4%

6M 4.5%

1Y 4.8%

2Y 5.1%

3M 3.2%

6M 3.8%

1Y 4.2%2Y 4.5%


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Suppose the current LIBOR discount factors P(0,tj) aregiven by the table below.

Calculate the annual nominal interest rate

compounded quarterly for a loan for the followingmaturity dates: 3, 6, 9 and 12 months.

Problem 5

LIBOR discount rates

P(0,tj) 0.9869 0.9739 0.9611 0.9482

Time in months 3 6 9 12

07 interest rates swaps

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