Advanced Derivatives: swaps beyond plain vanilla Structured notes exotic options

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
Examples 1) European Gap call option, with
G0
PayoffT
Payoffs ST - G if ST gt K 0
if ST lt K
K
2) digital European call
Payoffs K if ST gt K 0
if ST lt K
K ST
3
Range Binary options
Example 1) binary /DM range option with
range ( .56, .575)
PayoffT
Payoff 3x premium if .56 lt ST lt .575 0
if ST lt .56 or ST gt .575
Typical underlying exchange rates, interest
rates commodity prices
3x premium
0.56 0.575 ST
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 (Bankers Trust 1996)
binary quad-range option four ranges!
PayoffT
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! ST
Note this allows sale of volatility with limited
loss (as opposed to sale of straddle)
5
Rainbow Options
6
Asian (Average price) Options
Average94.75
Option life (averaging period 180 days)
7
Barrier Options down and out
Lower barrier
Option ceases to exist
8
Barrier Options down and in
Lower barrier
Lower barrier
Option is activated
9
Up and out knockout put
Knockout upper barrier
Option ceases to exist