1. April, 2008 Exotic Option Modeling Matt Simpson, CME Group

2. 2 What are exotics used for? Similar to vanilla options in many respects. Allow new variations of the basic In-the-money / Out-of-the- money paradigm to be modeled. Used in both Exchange and OTC settings. Usually are “options on cash” although may also be “options on futures” or even “option on physical”. Used as a substitute for complex option spreads. Can be used to mimic other risk mitigation mechanism such as Insurance Loss Warranties (ILW’s). Rapid payouts following a triggering event. More closely attuned to an investors view of the market Exotic Option Modeling

3. 3 Payout Type is an important aspect of exotic options: Payout Types Fixed Payout – The payout amount is specified at inception. Associated with Digital options (Yes, it pays or No, it doesn’t pay) Capped Payout – The payout amount is capped based on the difference between the strike and a cap price for call options and a floor price for put options Vanilla Payout – The payout amount is determined by the difference between the strike and the underlying Exotic Option Modeling

4. 4 Simple Exotic Option Types Digital – fixed pay out when the underlying price reaches a predefined trigger price Digital Range – fixed pay out if the underlying settles between an upper and lower trigger price Digital All-or-None – fixed pay out if the underlying settles on a predefined trigger price Digital One-Touch – immediate fixed pay out if the underlying reaches the predefined trigger price at any point during the life of the instrument Note that the Exercise Style will determine the timing of the payout. American style options pay-out if exercised European style options pay out only at expiration One-Touch options pay out immediately Bermuda style pay out only on specified dates Exotic Option Modeling

5. 5 Simple Exotic Option Types Barrier - The option becomes active* (knock-in) or inactive** (knock-out) based on a predetermined barrier price. – Barriers can be applied to a variety of payout types – *Active=Eligible for exercise, **Inactive=Ineligible for exercise Up-and-In – The option becomes active if the underlying price exceeds the specified barrier. Up-and-Out – the option becomes inactive if the underlying price exceeds the specified barrier. Down-and-Out – The option becomes inactive if the underlying price drops below the specified barrier. Down-and-In – the option becomes active if the underlying price drops below the specified barrier. Exotic Option Modeling

6. 6 Simple Exotic Option Types Capped Call – The option has a linear payout (like a vanilla) up to a capped amount as specified by a cap price Floored Put – The option has a linear payout (like a vanilla) up to a capped amount as specified by a floor price Asian – The underlying price is an average of the daily settlement prices over a specified period. Average – The strike price is an average of the daily settlement prices over a specified period. Look-back – The underlying price is set to the optimal value of the daily settlement prices over a specified period. Exotic Option Modeling

7. 7 Complex Exotic Option Types Double Barrier – An option that has a combination of activation/inactivation conditions. Any combination of down/out, up/out, down/in, up/in may be used Multi-barrier options are implemented using “or” conditions; Barrier1 or Barrier2 will go into effect, but not both. Digital Barrier – A digital option which becomes active or inactive based on the crossing of a barrier. Events are linked through “And” condition Capped Barrier – A capped option which becomes active or inactive based on the crossing of a barrier. Capped Asian – A capped option which pays out based on the average price of the underlying These are just a few examples. Many other combinations are possible Exotic Option Modeling

8. 8 Barrier Options Graph A - An option hits an initial down-and-out barrier and is inactivated. Even as the underlying price rises back through the barrier it remains inactive. Graph B - An option does not hit the down-and-out barrier, remains active, and culminates in a pay out.

9. 9 Barrier Options Up-and-In Call Graph A - An option fails to hit the up-and-in barrier and remains inactive regardless of being in-the-money. Graph B - An option hits the up-and-in barrier, activates, and remains active even when falling below the barrier. Up and In

10. 10 Double Barrier Options Up and In Graph A - An option hits an initial down-and-out barrier and is inactivated. Later, as the underlying price rises the option hits an up-and-in barrier and is re-activated. Graph B - An option hits the up-and-in barrier and is activated. When it dips below the barrier it remains active. If the underlying price falls far enough it may cross the down-and-out barrier a second time and become inactivated once again if specified Up and In

11. 11 Modeling Approach Provide a generic approach to representing extended options behavior Allow “exotic” behaviors to be handled using standardized “events” Events support flexibility and extensibility “Event Group” allows any number of exotic events to be specified – Events can be conditionally linked; “and” (digital barrier), “or” (double barrier) Maintains the old StrikePrice/PutCall concept in order to minimize disruption Business key becomes diluted as Events must now be included. – SubTyp as potential “summary” field Exotic Option Modeling

12. 12 Root-level Attributes SecurityType (SecTyp) – OOP, OOF, OPT SecuritySubType (SubTyp) – Digital, Barrier, Capped, etc PutOrCall (PutCall) – Put, Call StrikePrice (Strk) – ExerciseStyle (ExerStyle) – American, European, Bermuda StrikePxDeterminationMethod – fixed, average, set to underlying at expiration (look-back floating), set to optimal value StrikePxBoundaryMethod –, >= (vs underlying) UnderlyingPxDeterminationMethod – regular, special reference, optimal value (Lookback), average value (Asian) PayOutType (POTyp) – Vanilla, Digital, Capped PayOutAmount (POAmt) – $ Exotic Option Modeling

13. 13 Event Price Repeating Group Attributes (order of events is determined by sequence of instances) EventPriceType (EvtPxTyp) – Trigger, Capped, Knock-in Up, Knock- in Down, Knock-out Up, Knock-out Down EventPrice (EvtPx) – EventPxBoundaryMethod –, >= (vs underlyling) EventPxTimeType – Expiration, Immediate, Specified Time EventCondition – And, Or – And = Conditions can be in effect concurrently – Or = Conditions are mutually exclusive EventDateGroup EventTimeGroup Exotic Option Modeling

14. 14 Event Date/Time Repeating Group Attributes EventDateGroup – used to indicate specific dates or date ranges for which an event is in effect. EventTimeGroup – used to indicate specific times. If necessary, a TimeGroup can be associated with a DateGroup if necessary EventDateGroup – StartDate - YYYYMMDD-HHMMSS.sss – EndDate – YYYYMMDD-HHMMSS.sss EventTimeGroup – StartTime – HHMMSS.sss – EndTime – HHMMSS.sss Exotic Option Modeling

15. 15 Structure of an Exotic Option Exotic Option Modeling SecurityType SecuritySubType PutOrCall StrikePx ExerciseStyle PayOutType PayOutAmount StrikePxDetermination StrikPxBoundaryMeth UndlyPxDetermination EventPriceType, EventPrice EventPxBoundaryMeth, EventPxTimeType Event Condition Base Option Attributes Pay Out Attributes Option Event Attributes EventPriceType, EventPrice EventPxBoundaryMeth, EventPxTimeType Event Condition Event Date and Time Attributes EventDateGroup StartDate EndDate

16. 16 Structure of an Exotic Option Exotic Option Modeling SecTyp=OOP SubTyp=Digital PutCall=C Strk=12345 ExerStyle=European PayOutType=Digital PayOutAmount=10,000 StrikePxDetermination StrikPxBoundaryMeth UndlyPxDetermination=Reg Base Option Attributes Pay Out Attributes Option Event Attributes EventDateGroup StartDate EndDate Event Date and Time Attributes EventPriceType=Knock-in Up EventPrice=12350 EventPxBoundaryMeth >= EventPxTimeType=Immediate EventPriceType=Knock-out Down EventPrice=12340 EventPxBoundaryMeth >= EventPxTimeType=Immediate EventPriceType=Trigger EventPrice=12345 EventPxBoundaryMeth >= EventPxTimeType=Expiration Digital Barrier

17. 17 Hurricane Digital <Instrmt SecTyp= OOP SubTyp= Digital PutCall = Call Strk= 100.0 ExerStyle= American UndPxDetMeth= Regular PayOutTyp= Digital PayOutAmt= 10,000 > Exotic Option Modeling Instrument Definition Examples <EventPx EventPxTyp= Trigger EventPx= 100.0 EventPxBndryMeth= >= EventPxTimeTyp= Expiration />

18. 18 Euro FX Double Barrier <Instrmt ID= EC MMY= 200809 SecTyp= OOF SubTyp= Barrier PutCall = Call Strk=13350.0 ExerStyle= European UndPxDetMeth= Regular PayOutTyp= Vanilla > Exotic Option Modeling Instrument Definition Examples <EventPx EventPxTyp= Knock-out down EventPx= 13300.0 EventPxBndryMeth= <= EventPxTimeTyp= Immediate /> <EventPx EventPxTyp= Knock-in up EventPx= 13370.0 EventPxBndryMeth= >= EventPxTimeTyp= Immediate />

19. 19 Euro FX Capped Call – One Touch <Instrmt ID=EC MMY= 200809 SecTyp= OOP SubTyp= Cap PutCall = Call Strk= 13350.0 ExerStyle= European UndPxDetMeth= Regular PayOutTyp= Capped > Exotic Option Modeling Instrument Definition Examples <EventPx EventPxTyp= Capped EventPx= 13400.0 EventPxBndryMeth= >= EventPxTimeTyp= Immediate />