1

Advanced Derivatives:(plain vanillaplain vanilla to RRaaiinnbboowwss)advanced swapsStructured notesexotic options

S. Mann, 2006

2

Equity Swaps

Example: Thai Bank prohibited from holding domestic equityBank circumvents regulation with total return swap:Thai bank buys US government securitiesTiger fund buys Thai equityEnter into total return swap: returns swapped, not asset.

Thai Financial Institution

Tiger Fundor otherHedge Fund

US Bond return

Thai equity return

Return details (what currency?) denoted by distinct swap names

3

Asset swaps: Quantos

Total return swap with exchange rate risk eliminatedPayments determined by total return on different assets,multiplied by notional principal in one currency.

U.S. Global

Portfolio

FrenchPension

Fund

S&P 500 total return x Notional Principal

(CAC-40 return + spread) x Notional principal

Payment details on next slide

Example: swap S&P 500 for CAC-40 (France) + spread

4

Quanto swap outcome example

Quanto swap: Pay S&P 500 return, receive CAC-40 + swap spread

Notional principal ($millions) 25 payments all in dollarsswap spread (basis points) 70

S&P 500 CAC-40 spread net

date days index % ret payment index % ret payment payment payment

2/17/98 955 2230

5/15/98 88 964 0.94% 235,027 2179 -2.3% -564,964 42,778 (757,213)

8/17/98 92 986 2.24% 558,759 2536 16.4% 4,093,328 44,722 3,579,291

11/16/98 89 1032 4.65% 1,162,832 2514 -0.9% -215,181 43,264 (1,334,749)

2/16/99 90 1012 -1.86% -463,847 2681 6.6% 1,653,370 43,750 2,160,967

day count = actual/360

total return

S&P 500 CAC-40 (France)

total return

A possible sequence of events

5

Equity Collars

Col

lar

valu

e (%

of

orig

inal

sto

ck p

rice

) +25%

-10%

LongStock

ST

Stock plus collar

Monetarize position withoutrealizing gain.

Zero-cost collar:sell call to pay for put:choose put so that losspossibility at least 10%.(Investor is “at risk”, not anIRS “constructive sale”).

Borrow against hedged position at advantageous rate (Libor + 100 bp).Standard contracts available for large ($2 million) positions in liquid stock.

Longer the term, higher upside percentage available.

Cite: Braddock, 1997, “Zero-cost Collars,” Risk, November 1997.

6

Swap floating for floating

Basis Swap:

T-billPayer

Libor payer

T-bill rate

Libor - spread

Constant Maturity swap

Constant MaturityPayer

Liborpayer

Libor + spread

Five-year T-noteConstant maturity yield

7

Amortizing swap

Notional principal reduced over time (e.g. mortgage)

T1 T2 T3 T4

N1

N2

N3

N4

Valuation:0 = B(0,T1)(SFR - F1)N1 + B(0,T2)(SFR - F2)N2

+ B(0,T3)(SFR - F3)N3+ B(0,T4)(SFR - F4)N4

where Ft = appropriate forward rateSFR = swap fixed rate

8

Diff swaps: (currency hedged basis swap)

Floating for floating swapFloating rates are in different currenciesAll swap payments in one currency

U.S. Firmdesiringexposure

to UK yield

U.S Firmreducingexposure

to UK yield(5 -year CMT yield) x Notional principal ($)

(5-year £ gilt yield) x Notional principal ($)

Example: swap 5 year gilt (£) yield for 5 year CMT T-note yield swap payments in $

9

Commodity derivatives

Commodity-linked loans Merrill Lynch - $250 mil Aluminum-linked bond for Dubal (Barrick)Price protection standard for project financing

hedging to assure break-even as loan requirement.Gold hedging used to raise LBO funds.Gas swaps

Basis swaps (Enron)Oil swaps

Crack Spread swaps

10

Credit derivatives

First generation: Bankers Trust (BT) and Credit Suisse (CS) notes (Japan 1993)objective: free up credit lines to Japanese financial sectornote payoffs: coupon = Libor + 100 bp ; but: coupon and principal reduced if defaults occur.

one lego (building block) is credit default swap:

ProtectionBuyer

ProtectionSeller

Notional Principal x (40 bp)

Floating payment contingent on defaults;payment mirrors loss incurred by creditors

Contingent payment based on post-default value of reference security

11

Enron Credit default swaps – Fall 2001

Enron Credit Default Swaps Bid/Offer Band (basis points)

0

200

400

600

800

1000

1200

1400

8/1/01

8/8/01

8/15/01

8/22/01

8/29/01

9/5/01

9/12/01

9/19/01

9/26/01

10/3/01

10/10/01

10/17/01

10/24/01

10/31/01

11/7/01

11/14/01

11/21/01

120 Month Maturity 60 Month Maturity 12 Month Maturity

12

GM Credit default swaps: 2002-2004

13

GM Credit default swaps – Fall 2005

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Structured notes: Range Floaters(Range contingent accrual bonds)

Bonds that accrue interest only on days when range conditions satisfied.

Example:$10 million bond: 12% coupon, accrual range contingent;range is ($.50, $.59) $/DMsemiannual coupon =

$10m x (.12) x ( (days within range)/365)(this is a restart accrual; can be barrier terminal accrual)

15

Structured notes - Inverse floater

Example:GNMA 10-year note; maturity 12/15/07coupon paid semi-annually: 6/15 and 12/15coupon = max(0.02, (0.18- 2xLibor)) x (180/360) x Facecoupon on $1 million note a function of Libor:Libor coupon.050 40,000.055 35,000.060 30,000.070 20,000.080 10,000.090 10,000

5% 6% 7% 8% 9% Libor

Coupon

40,000

30,000

20,000

10,000

T-note coupon

Floater coupon

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Exotic options

Binaries: Digital ; Gap ; Ranges. Chooser (as you like it) Rainbow (welcome to OZ) option on best of twoAsian (average price or average strike)Bermudan (exercise windows)Lookback (no regret)barrier options:

knockouts: up and out; down and outKnockins: up and in; down and in

many, many more, including“Down and in” Arrow, or Arrow-Debreu (advanced*)

(* see Carr and Chou, 1997, RISK magazine, vol 10 #9)

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Digital and Gap options

K ST

K

Examples:1) European Gap call option, with G=0

PayoffT

2) digital European call

Payoffs:ST - G if ST > K0 if ST < K

Payoffs:K if ST > K0 if ST < K

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Range Binary options

$0.56 $0.575 ST

3x premium

Example:1) binary $/DM range option with range = ( $.56, $.575)

PayoffT

Payoff:3x premium if $.56 < ST < $.5750 if ST < $.56 or ST > $.575

Typical underlying:exchange rates, interest ratescommodity prices

Usage example: Corp long DM, buys put and range. Outcomes: 1) DM up : gain on long DM position

2) DM down: hedged with put

3) unchanged: range pays off, pays for put.

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Quattro option (Banker’s Trust 1996)

All four ranges! ST

8x premiumbinary quad-range option: four ranges!

PayoffT

Payoff:8x premium if all four ranges unbroken6xpremium if only one range broken4xpremium if two ranges unbroken2xpremium if only one range unbroken0 if all ranges broken

Note this allows sale of volatilitywith limited loss (as opposed to sale of straddle)

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Rainbow Options

Rainbow option: Option on best of two assets

$0

$20

$40

$60

$80

$100

$120

$140

$160

$180

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185 193 201 209 217 225 233 241 249

Time (days)

as

se

t p

ric

es

Asset A

Asset B

Option payoff = max(0, AT-K,BT-K)if K=$100; AT = 110; BT = $143Rainbow payoff = $43

21

Asian (Average price) Options

Price history for Asian option payoff

0

20

40

60

80

100

120

140

1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 221 232 243

Time (days)

As

se

t p

ric

e

Option life (averaging period= 180 days)

Average=94.75

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Barrier Options: down and out

Down and Out call option

0

20

40

60

80

100

120

1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 221 232 243

Time (days)

Ass

et p

rice

Lower barrier

Option ceases to exist

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Barrier Options: down and in

Lower barrier

Down and In put option

0

10

20

30

40

50

60

70

80

90

1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 221 232 243

Time (days)

As

se

t p

ric

e

Lower barrier

Option isactivated

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Up and out knockout put

Up and Out Put Option

0

20

40

60

80

100

120

1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 221 232 243

Time (days)

As

se

t p

ric

e

Knockout upper barrier

Option ceases to exist