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1 plain vanilla Rainbows Advanced Derivatives: (plain vanilla to Rainbows ) advanced swaps Structured notes exotic options S. Mann, 2006

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

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

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4 Quanto swap outcome example A possible sequence of events

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5 Equity Collars Collar value (% of original stock price) +25% -10% Long Stock STST 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. Cite: Braddock, 1997, “Zero-cost Collars,” Risk, November 1997.

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6 Swap floating for floating Basis Swap: T-bill Payer Libor payer T-bill rate Libor - spread Constant Maturity swap Constant Maturity Payer Libor payer Libor + spread Five-year T-note Constant maturity yield

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7 Amortizing swap Notional principal reduced over time (e.g. mortgage) T 1 T 2 T 3 T 4 N1N1 N2N2 N3N3 N4N4 Valuation: 0 = B(0,T 1 )(SFR - F 1 )N 1 + B(0,T 2 )(SFR - F 2 )N 2 + B(0,T 3 )(SFR - F 3 )N 3 + B(0,T 4 )(SFR - F 4 )N 4 where F t = appropriate forward rate SFR= swap fixed rate

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8 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 swap payments in $

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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

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10 Credit derivatives First generation: Bankers Trust (BT) and Credit Suisse (CS) notes (Japan 1993) objective: free up credit lines to Japanese financial sector note payoffs: coupon = Libor + 100 bp ; but: coupon and principal reduced if defaults occur. one lego (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 Contingent payment based on post-default value of reference security

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11 Enron Credit default swaps – Fall 2001

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12 GM Credit default swaps: 2002-2004

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13 GM Credit default swaps – Fall 2005

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14 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 ( (days within range)/365) (this is a restart accrual; can be barrier terminal accrual)

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15 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: Liborcoupon.05040,000.05535,000.06030,000.07020,000.08010,000.09010,000 5% 6%7%8%9% Libor Coupon 40,000 30,000 20,000 10,000 T-note coupon Floater coupon

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

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17 Digital and Gap options KSTKST K Examples: 1) European Gap call option, with G=0 Payoff T 2) digital European call Payoffs: S T - G if S T > K 0 if S T < K Payoffs: K if S T > K 0 if S T < K

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18 Range Binary options $0.56 $0.575S 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 $.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 3) unchanged: range pays off, pays for put.

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19 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 with limited loss (as opposed to sale of straddle)

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20 Rainbow Options

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21 Asian (Average price) Options Option life (averaging period= 180 days) Average=94.75

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22 Barrier Options: down and out Lower barrier Option ceases to exist

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23 Barrier Options: down and in Lower barrier Option is activated

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24 Up and out knockout put Knockout upper barrier Option ceases to exist

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