1 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)

2 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

3 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 < $ 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.

4 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)

5 Rainbow Options

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

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

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

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