Finance 70520. Spring 2002 The Neeley School of Business at TCU Steven C. Mann, 2002.
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Advanced Derivatives: ( plain vanilla plain vanilla to R R a a i i n n b b o o w w s s) advanced swaps Structured notes exotic options inance 70520. Spring 2002 he Neeley School of Business at TCU Steven C. Mann, 2002.
description
Advanced Derivatives: ( plain vanilla to R a i n b o w s ) advanced swaps Structured notes exotic options. Finance 70520. Spring 2002 The Neeley School of Business at TCU Steven C. Mann, 2002. Equity Swaps. Example: Thai Bank prohibited from holding domestic equity - PowerPoint PPT Presentation
Transcript of Finance 70520. Spring 2002 The Neeley School of Business at TCU Steven C. Mann, 2002.
Advanced Derivatives:(plain vanillaplain vanilla to RRaaiinnbboowwss)advanced swapsStructured notesexotic options
Finance 70520. Spring 2002The Neeley School of Business at TCUSteven C. Mann, 2002.
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
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
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
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 ($2 million) positions in liquid stock.
Longer the term, higher upside percentage available.
Cite: Braddock, 1997, “Zero-cost Collars,” Risk, November 1997.
Swap floating for floating
Basis Swap:
T-billPayer
Libor payer
T-bill rate
Libor - spread
Constant Maturity swap
Constant MaturityPayer
Liborpayer
Libor + spread
Five-year T-noteConstant maturity yield
Amortizing swap
Notional principal reduced over time (e.g. mortgage)
T1 T2 T3 T4
N1
N2
N3
N4
Valuation:0 = B(0,T1)(SFR - F1)N1 + B(0,T2)(SFR - F2)N2
+ B(0,T3)(SFR - F3)N3+ B(0,T4)(SFR - F4)N4
where Ft = appropriate forward rateSFR = swap fixed rate
Diff swaps: (currency hedged basis swap)
Floating for floating swapFloating rates are in different currenciesAll swap payments in one currency
U.S. Firmdesiringexposure
to UK yield
U.S Firmreducingexposure
to UK yield(5 -year CMT yield) x Notional principal ($)
(5-year £ gilt yield) x Notional principal ($)
Example: swap 5 year gilt (£) yield for 5 year CMT T-note yield swap payments in $
Commodity derivatives
Commodity-linked loans Merrill Lynch - $250 mil Aluminum-linked bond for DubalPrice 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
Credit derivatives
First generation: Bankers Trust (BT) and Credit Suisse (CS) notes (Japan1993)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
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)
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
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)
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
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.
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)
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
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
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
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
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
