Advanced Derivatives:

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Barnaby Miles
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1 Advanced Derivatives: (plain vanilla to Rainbows) advanced swaps Structured notes exotic options Finance Spring 1999 The Neeley School of Business at TCU Steven C. Mann, 1999.

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 Thai equity return US Bond return Tiger Fund or other Hedge Fund Return details (what currency?) denoted by distinct swap names

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. 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

4 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/ /15/ % 235, % -564,964 42,778 (757,213) 8/17/ % 558, % 4,093,328 44,722 3,579,291 11/16/ % 1,162, % -215,181 43,264 (1,334,749) 2/16/ % -463, % 1,653,370 43,750 2,160,967

5 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 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-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

7 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

8 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

9 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

10 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 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

11 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)

12 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 ,000 Coupon ,000 40, , ,000 30, ,000 20, ,000 10,000 T-note coupon Floater coupon 5% 6% 7% 8% 9% Libor

13 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)

14 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

15 Range Binary options Example: 1) binary $/DM range option with range = ( $.56, $.575) Payoff T Payoff: 3x premium if $.56 < S T < $ 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.

16 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)

17 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 = $ Time (days)

18 Asian (Average price) Options Price history for Asian option payoff Asset price Average=94.75 Option life (averaging period= 180 days) Time (days)

19 Barrier Options: down and out Down and Out call option Asset price Option ceases to exist Lower barrier Time (days)

20 Barrier Options: down and in Down and In put option Asset price Option is activated Lower barrier Lower barrier Time (days)

21 Up and out knockout put Up and Out Put Option 120 Asset price Option ceases to exist Knockout upper barrier Time (days)

Swaps: complex structures

Swaps: complex structures Complex swap structures refer to non-standard swaps whose coupons, notional, accrual and calendar used for coupon determination and payments are tailored made to serve client