Advanced Derivatives:

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Advanced Derivatives:

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plain vanilla

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advanced swaps

Structured notes

exotic options

Finance 7523. Spring 1999

The Neeley School of Business at TCU

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S.Mann, 1999

Equity Swaps

Example:

Thai Bank prohibited from holding domestic equity Bank circumvents regulation with total return swap: Thai bank buys US government securities

Tiger fund buys Thai equity

Enter into total return swap: returns swapped, not asset.

Thai Financial Institution Tiger Fund or other Hedge Fund US Bond return Thai equity return

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Asset swaps: Quantos

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

U.S. Global Portfolio French Pension Fund

S&P 500 total return x Notional Principal

(CAC-40 return + spread) x Notional principal

Payment details on next slide

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S.Mann, 1999

Quanto swap outcome example

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

Notional principal ($millions) 25 payments all in dollars

swap 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)

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Equity Collars

Collar value

(% of original stock price)

+25%

-10%

Long Stock

S_T Stock plus collar

Monetarize position without realizing gain.

Zero-cost collar:

sell call to pay for put: choose put so that loss possibility at least 10%. (Investor is “at risk”, not an IRS “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.

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Swap floating for floating

Basis Swap: T-bill Payer Libor payer T-bill rate Libor - spread

Constant Maturity swap

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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

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Diff swaps: (currency hedged basis swap)

Floating for floating swap

Floating rates are in different currencies All swap payments in one currency

U.S. Firm desiring exposure to UK yield U.S Firm reducing exposure 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

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Commodity derivatives

Commodity-linked loans

Merrill Lynch - $250 mil Aluminum-linked bond for Dubal 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

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Credit derivatives

First generation:

Bankers Trust (BT) and Credit Suisse (CS) notes (Japan1993) objective: free up credit lines to Japanese financial sector

note payoffs:

coupon = Libor + 100 bp ;

but: coupon and principal reduced if defaults occur. Basic leggo (building block) is credit default swap:

Protection Buyer

Protection Seller

Notional Principal x (40 bp)

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

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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) $/DM

semiannual coupon =

$10m x (.12) x (

ΣΣ

(days within range)/365)

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S.Mann, 1999

Structured notes - Inverse floater

Example:

GNMA 10-year note; maturity 12/15/07 coupon paid semi-annually: 6/15 and 12/15

coupon = max(0.02, (0.18- 2xLibor)) x (180/360) x Face coupon on $1 million note a function of Libor:

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Exotic options

Binaries: Digital ; Gap ; Ranges. Chooser (as you like it)

Rainbow (welcome to OZ) option on best of two Asian (average price or average strike)

Bermudan (exercise windows) Lookback (no regret)

barrier options:

knockouts: up and out; down and out Knockins: up and in; down and in many, many more, including

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

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Digital and Gap options

K S_T

K Examples:

1) European Gap call option, with G=0

Payoff_T

2) digital European call

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Range Binary options

$0.56 $0.575 S_T 3x premium

Example:

1) binary $/DM range option with range = ( $.56, $.575) Payoff_T Payoff: 3x premium if $.56 < S_T < $.575 0 if S_T< $.56 or S_T > $.575 Typical underlying:

exchange rates, interest rates commodity 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

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Quattro option (Banker’s Trust 1996)

All four ranges! S_T 8x premium

binary quad-range option: four ranges!

Payoff_T

Payoff:

8x premium if all four ranges unbroken

6xpremium if only one range broken

4xpremium if two ranges unbroken 2xpremium if only one range unbroken 0 if all ranges broken

Note this allows sale of volatility

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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) asset prices Asset A Asset B

Option payoff = max(0, A_T-K,B_T-K) if K=$100; A_T= 110; B_T = $143

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S.Mann, 1999

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) Asset price

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Barrier Options: down and out

Down and Out call option

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Barrier Options: down and in

Lower barrier Down and In put option

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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) Asset price

Knockout upper barrier