Advanced Derivatives plain vanilla to Rainbows advanced swaps

Advanced Derivatives: (plain vanilla to Rainbows) 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 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 (CAC-40 return + spread) x Notional principal U. S. Global Portfolio French Pension Fund S&P 500 total return x Notional Principal Payment details on next slide

Quanto swap outcome example A possible sequence of events

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 Monetarize position without realizing gain. (% of original stock price) Equity Collars +25% Long Stock plus collar -10% ST 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: Libor - spread T-bill Payer Libor payer T-bill rate 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 T 1 T 2 T 3 N 4 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 Ft 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 $ (5 -year £ gilt yield) x Notional principal ($) U. S. Firm desiring exposure to UK yield U. S Firm reducing exposure to UK yield (5 -year CMT yield) x Notional principal ($)

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 (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 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 = $10 m 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 - 2 x. Libor)) x (180/360) x Face coupon on $1 million note a function of Libor: Libor coupon Coupon. 050 40, 000. 055 35, 000 T-note coupon. 060 30, 000. 070 20, 000. 080 10, 000 Floater coupon. 090 10, 000 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: ST - G 0 if ST > K if ST < K Payoff. T K 2) digital European call Payoffs: K 0 if ST > K if ST < K K ST

Range Binary options Example: 1) binary $/DM range option with range = ( $. 56, $. 575) Payoff. T Payoff: 3 x premium if $. 56 < ST < $. 575 0 if ST < $. 56 or ST > $. 575 Typical underlying: exchange rates, interest rates commodity prices 3 x premium $0. 56 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. $0. 575 ST

Quattro option (Banker’s Trust 1996) binary quad-range option: four ranges! Payoff: 8 x premium 6 xpremium 4 xpremium 2 xpremium 0 Payoff. T 8 x premium if all four ranges unbroken if only one range broken if two ranges unbroken if only one range unbroken if all ranges broken All four ranges! Note this allows sale of volatility with limited loss (as opposed to sale of straddle) ST