Ch 07 Hull Fundamentals 8 the d

7/25/2019 Ch 07 Hull Fundamentals 8 the d

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Options, Futures, and Other Derivatives, 8th Ed, Ch 7, Copyright John C. Hull 20!

Swaps

Chapter 7

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Nature of Swaps

A swap is an agreement to

exchange cash flows at specifiedfuture times according to certainspecified rules

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An Example of a Plain Vanilla

Interest Rate Swap

An agreement by Microsoft to receive6-month LI!" # pay a fixed rate of

$% per annum every 6 months for &years on a notional principal of '())million

*ext slide illustrates cash flows thatcould occur +,ay count conventionsare not considered

Options, Futures, and Other Derivatives, 8th Ed, Ch 7, Copyright John C. Hull 20!3


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---------Millions of ,ollars---------

LI!" F"O#$%&' F%(ED *et

,ate "ate Cash .low Cash .low Cash .low

Mar/$0 1)(& 2/1%

3ept/ $0 1)(& 2/4% 51/() 1/$) )/2)

Mar/$0 1)(2 $/&% 51/2) 1/$) )/()

3ept/ $0 1)(2 $/$% 51/6$ 1/$) 5)/($

Mar/$0 1)($ $/6% 51/7$ 1/$) 5)/1$

3ept/ $0 1)($ $/% 51/4) 1/$) 5)/&)

Mar/$0 1)(6 6/2% 51/$ 1/$) 5)/2$

Cash Flows to MicrosoftSee !a"le #$%& pa'e %()

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!*pical +ses of an

Interest Rate Swap

Converting a liability from

fixed rate to floating rate floating rate to fixed rate

Converting an investment from fixed rate to floating rate floating rate to fixed rate

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Intel an, Microsoft MS-

!ransform a .ia"ilit*

Fi'ure #$/& pa'e %(%-

Intel MS

LIBOR

5%

LIBOR+0.1%

5.2%

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Financial Institution is In0ol0e,

Fi'ure #$1& pa'e %(2-

F.I.

LIBOR LIBOR

LIBOR+0.1%

4.985% 5.015%

5.2%

Intel MS

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Intel an, Microsoft MS-

!ransform an AssetFi'ure #$2& pa'e %(/-

Intel MS

LIBOR

5%

LIBOR0.2%

4.7%

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Financial Institution is In0ol0e,See Fi'ure #$3& pa'e %(2-

Intel F.I. MS

LIBOR LIBOR

4.7

%

5.015%4.985%

LIBOR0.2%

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4uotes 5* a Swap Mar6et Ma6er!a"le #$2& pa'e %(1-

Maturity id +% !ffer +% 3wap "ate +%

1 years 6/)& 6/)6 6/)2$

& years 6/1( 6/12 6/11$

2 years 6/&$ 6/& 6/&7)

$ years 6/27 6/$( 6/2)

7 years 6/6$ 6/64 6/66$

() years 6/4& 6/47 6/4$)

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7a* Count

A day count convention is specified for forfixed and floating payment

.or example0 LI!" is li8ely to beactual9&6) in the :3 because LI!" is amoney mar8et rate



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Confirmations

Confirmations specify the terms of atransaction

;he International 3waps and ,erivatives

has developed Master Agreements thatcan be used to cover all agreementsbetween two counterparties

Central clearing is used for most standardswaps



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!he Comparati0e A,0anta'e

Ar'ument !a"le #$1& pa'e %((-

AAACorp wants to borrow floating Corp wants to borrow fixed

Fi)ed Floating

AAACorp 2/))% 6-month LI!" < )/(%

Corp $/1)% 6-month LI!" 5 )/6%

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!he Swap Fi'ure #$(& pa'e %(#-

AAACorp BBBCorp

LIBOR

LIBOR+0.6%

4.35%

4%

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!he Swap when a Financial

Institution is In0ol0e,Fi'ure #$#& pa'e %(8-

AAA F.I. BBB4%

LIBOR LIBOR

LIBOR+0.6%

4.33% 4.37%

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Criticism of the Comparati0e

A,0anta'e Ar'ument

;he 2/)% and $/1% rates available to AAACorpand Corp in fixed rate mar8ets are $-yearrates

;he LI!"


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!he Nature of Swap Rates

3ix-month LI!" is a short-term AAborrowing rate

;he $-year swap rate has a ris8corresponding to the situation where () six-month loans are made to AA borrowers atLI!"

;his is because the lender can enter into a

swap where income from the LI!" loans isexchanged for the $-year swap rate

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90erni'ht In,exe, Swaps

.ixed rate for a period is exchanged for thegeometric average of the overnight rates

3hould the !I3 rate e>ual the LI!" rate? A

ban8 can orrow '()) million in the overnight mar8et0 rolling

forward for & months @nter into an !I3 swap to convert this to the &-

month !I3 rate Lend the funds to another ban8 at LI!" for &

months



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90erni'ht In,exe, Swaps continue,

///but it bears the credit ris8 of another ban8 in thisarrangement

;he excess of LI!" over the !I3 rate is the

LI!"-!I3 spread/ It is usually about () basispoints but spi8ed at an all time high of &62 basispoints in !ctober 1))4



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9IS 0s .I59R ,iscountin'

;raditionally LI!" rates +and swap ratesdetermined from swaps where LI!" isexchanged for fixed have been used as ris8-

free rates when derivatives are valuedMost mar8et participants now use the !I3

rate as the discount rate when collateralieddeals are valued0 but continue to use LI!"rates for discounting cash flows in non-collateralied deals



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+sin' Swap Rates to 5ootstrap the

.I59R:Swap ;ero Cur0e when

.I59R ,iscountin' is use, Consider a new swap where the fixed rate is the swap

rate Bhen principals are added to both sides on the final

payment date the swap is the exchange of a fixed ratebond for a floating rate bond

;he floating-rate rate bond is worth par/ ;he swap isworth ero/ ;he fixed-rate bond must therefore also beworth par

;his shows that swap rates define par yield bonds thatcan be used to bootstrap the LI!" +or LI!"9swapero curve

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Example of 5ootstrappin' the

.I59R:Swap Cur0e Example #$2& pa'e %#2-

6-month0 (1-month0 and (4-monthLI!"9swap rates are 2%0 2/$%0 and 2/4%with continuous compounding/

;wo-year swap rate is $% +semi-annual

;he 1-year LI!"9swap rate0 R0 is 2/$&%


1005.1025.25.25.2 25.1048.00.1045.05.004.0

=+++ R

eeee


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Valuation of an Interest Rate

Swap

Initially interest rate swaps are worthclose to ero

At later times they can be valued as a

portfolio of forward rate agreements+."As



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Example

"eceive six-month LI!"0 pay &% +s/a/compounding on a principal of '()) million

"emaining life (/1$ years LI!" rates for &-months0 -months and ($-

months are 1/4%0 &/1%0 and &/2% +cont comp 6-month LI!" on last payment date was 1/%

+s/a/ compounding



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Valuation Assumin' .I59R

7iscountin'

@ach exchange of payments in an interestrate swap is an ."A

;he ."As can be valued on theassumption that today=s forward rates arerealied

;he forward rates can be calculateddirectly from the LI!"9swap ero curve

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Forwar, Rates

;he forward rates with semiannualcompounding are &/21% for the & to month period &/7&2% for the to ($ month period



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Valuation of Example +sin' FRAs

an, .I59R ,iscountin' Example #$/ &pa'e %#/-

;ime .ixedcash flow

.loatingcash flow

*et Cash.low

,iscfactor

Dfl

)/1$ -(/$ 5(/2$)) -)/)$)) )/&) -)/)27

)/7$ -(/$ 5(/7(2$ 5)/1(2$ )/76& 5)/1)2

(/1$ -(/$ 5(/4671 5)/&671 )/$42 5)/&$(

;otal 5)/$((7



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Valuation in !erms of 5on,s

usin' .I59R ,iscountin'

;he fixed rate bond is valued in the usualway

;he floating rate bond is valued by notingthat it is worth par immediately after thenext payment date

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Value of Floatin' Rate 5on,

L


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Example Example #$(& pa'e %##-


;ime fixcash

flow

fl cash

flow

,iscfactor

Dfix

Dfl

)/1$ (/$))) ()(/2$)) )/&) (/24$ ())/721&

)/7$ (/$))) )/76& (/2622

(/1$ ()(/$))) )/$42 7/1766

;otal ())/1&)6 ())/721&

3wap value E ())/721& < ())/1&)6 E )/$((7


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Valuation of Swaps +sin' 9IS

,iscountin'

Fero rates are bootstrapped from !I3rates +;his is similar to the way theLI!"9swap ero curve is produced

.orward LI!" rates are then calculatedso that so that swaps entered into at thecurrent swap rate are worth ero +3ee

@xample 7/$0 page (76



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Valuation of Swaps +sin' 9IS

,iscountin'continue,

;he swap is valued by assuming thatforward LI!" is realied and discountingat the !I3 rate

;here is no simple way of valuing theswap in terms of bonds



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An Example of a Fixe,=for=Fixe,

Currenc* Swap

An agreement to pay $% on a sterlingprincipal of G()0)))0))) # receive 6%

on a :3' principal of '($0)))0)))every year for $ years

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Exchan'e of Principal

In an interest rate swap theprincipal is not exchanged

In a currency swap the

principal is exchanged at thebeginning and the end of theswap

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!he Cash Flows !a"le #$3& pa'e %8)-


,ate ,ollar Cash .lows+millions

3terling cash flow+millions

.eb (0 1)(( -($/)) 5()/))

.eb (0 1)(1 5)/)


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!*pical +ses of a

Currenc* Swap

Conversion from a liability in one currencyto a liability in another currency

Conversion from an investment in onecurrency to an investment in another

currency

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Comparati0e A,0anta'e Ma* 5e

Real 5ecause of !axes

Heneral @lectric wants to borrow A:, uantas wants to borrow :3,

Cost after adJusting for the differentialimpact of taxes


:3, A:,

Heneral @lectric $/)% 7/6%

uantas 7/)% 4/)%


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Valuationof Fixe,=for=Fixe,

Currenc* Swaps

.ixed for fixed currency swaps canbe valued either as the differencebetween 1 bonds or as a portfolio offorward contracts

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Example pa'es %8/=%81-

All Kapanese LI!"9swap rates are 2%All :3, LI!"9swap rates are % $% is received in yen 4% is paid in dollars/

ayments are made annually rincipals are '() million and (01)) million yen 3wap will last for & more years

Current exchange rate is (() yen per dollar



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Valuation in !erms of 5on,sExample #$#& pa'e %82-

;ime Cash .lows +' D +' Cash flows +yen D +yen

( )/4 )/7&(( 6) $7/6$

1 )/4 )/6641 6) $$/&& )/4 )/6()7 6) $&/11

& ()/) 7/6&&4 (01)) (0)62/&)

;otal /62& (01&)/$$


Dalue E (1&)/$$9(()


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Valuation in !erms of Forwar,sExample #$8& pa'e %81-


;ime ' cashflow

en cashflow

.orward@xch rate

en cashflow in '

*etCash.low

resentvalue

( -)/4 6) )/))$$7 )/$7&2 -)/1166 -)/1)7(

1 -)/4 6) )/)())27 )/6)14 -)/(71 -)/(627

& -)/4 6) )/)()$61 )/6&&7 -)/(66& -)/(16

& -()/) (1)) )/)()$61 (1/6726 51/6726 1/)2(7

;otal (/$2&)

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9ther Currenc* Swaps

.ixed-for-floatingN e>uivalent to a fixed-for-fixed currency swap plus a fixed forfloating interest rate swap

.loating-forfloatingN e>uivalent to a fixed-for-fixed currency swap plus two floatinginterest rate swaps



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Swaps > Forwar,s

A swap can be regarded as aconvenient way of pac8aging forwardcontracts

Bhen a swap is initiated the swap hasero value0 but typically some forwardshave a positive value and some have anegative value

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Cre,it Ris6

A swap is worth ero to a company initially At a future time its value is liable to be either positive or

negative

;he company has credit ris8 exposure only when itsvalue is positive 3ome swaps are more li8ely to lead to credit ris8

exposure than others Bhat is the situation if early forward rates have a

positive value? Bhat is the situation when the early forward rates have

a negative value?


C ,i 7 f l S A 4 i 6


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Cre,it 7efault Swaps? A 4uic6

First .oo6

*otional principal +e/g/ '()) million andmaturity +e/g/ $ yrs specified

rotection buyer pays a fixed rate +e/g/ ($) bp

on the notional principal +the C,3 spread If the reference entity +a country or company

defaults protection seller buys bonds issued bythe reference entity for their face value and the

spread payments stop/ ;otal face value of bondsbought e>uals notional principal



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9ther !*pes of Swaps

Amortiing9 step upCompounding swap

Constant maturity swapLI!"-in-arrears swapAccrual swap

@>uity swap

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9ther !*pes of Swaps continue,

Cross currency interest rate swap.loating-for-floating currency swap

,iff swapCommodity swapDariance swap

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Ch 07 Hull Fundamentals 8 the d