Advanced Derivatives: (plain vanilla to Rainbows) advanced swaps Structured notes exotic options Finance 7523. Spring 1999 The Neeley School of Business at TCU Steven C. 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 Thai equity return US Bond return Tiger Fund or other Hedge Fund Return details (what currency?) denoted by distinct swap names
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. Example: swap S&P 500 for CAC-40 (France) + spread U.S. Global Portfolio (CAC-40 return + spread) x Notional principal S&P 500 total return x Notional Principal French Pension Fund Payment details on next slide
Quanto swap outcome example A possible sequence of events 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 day count = actual/360 S&P 500 CAC-40 (France) total return S&P 500 total return 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
Equity Collars Long Stock 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 ). Collar value (% of original stock price) +25% -10% Stock plus collar S T 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-bill Payer Libor - spread T-bill rate Libor payer Constant Maturity swap Constant Maturity Payer Libor + spread Five-year T-note Constant maturity yield Libor payer
Amortizing swap Notional principal reduced over time (e.g. mortgage) N 1 N 2 N 3 N 4 T 1 T 2 T 3 T 4 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 SFR = appropriate forward rate = swap fixed rate
Diff swaps: (currency hedged basis swap) Floating for floating swap Floating rates are in different currencies All swap payments in one currency Example: swap 5 year gilt ( ) yield for 5 year CMT T-note yield swap payments in $ U.S. Firm desiring exposure to UK yield (5-year gilt yield) x Notional principal ($) (5 -year CMT yield) x Notional principal ($) U.S Firm reducing exposure to UK yield
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 Crack Spread swaps
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 Notional Principal x (40 bp) Protection Seller 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) $/DM semiannual coupon = $10m x (.12) x (S (days within range)/365) (this is a restart accrual; can be barrier terminal accrual)
Structured notes - Inverse floater Example: GNMA 10-year note; maturity 12/15/07 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: Libor coupon.050 40,000 Coupon.055 35,000 40,000.060 30,000.070 20,000 30,000.080 10,000 20,000.090 10,000 10,000 T-note coupon Floater coupon 5% 6% 7% 8% 9% Libor
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)
Digital and Gap options Examples: 1) European Gap call option, with G=0 Payoffs: S T - G if S T > K 0 if S T < K Payoff T K 2) digital European call Payoffs: K if S T > K 0 if S T < K K S T
Range Binary options 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 3x premium $0.56 $0.575 S T 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: S.Mann, range 1999 pays off, pays for put.
Quattro option (Banker s Trust 1996) binary quad-range option: four ranges! Payoff T 8x premium 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 All four ranges! S T Note this allows sale of volatility with limited loss (as opposed to sale of straddle)
Rainbow Options Rainbow option: Option on best of two assets $180 $160 $140 Asset A asset prices $120 $100 $80 $60 $40 $20 $0 Asset B Option payoff = max(0, A T -K,B T -K) if K=$100; A T = 110; B T = $143 Rainbow payoff = $43 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)
Asian (Average price) Options Price history for Asian option payoff Asset price 140 120 100 80 60 40 20 0 Average=94.75 Option life (averaging period= 180 days) 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)
Barrier Options: down and out Down and Out call option 120 100 Asset price 80 60 40 20 Option ceases to exist Lower barrier 0 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)
Barrier Options: down and in Down and In put option Asset price 90 80 70 60 50 40 30 20 10 0 Option is activated Lower barrier Lower barrier 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)
Up and out knockout put Up and Out Put Option 120 Asset price 100 80 60 40 20 Option ceases to exist Knockout upper barrier 0 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)