1. Introduction to Financial Engineering Aashish Dhakal Week 5: Exotics Option

2. Exotic Option Options European: On Expiry American: Any time exercise -These are plain Vanilla. -They have standard properties & trade actively. -Their Price are quoted in EXCHANGE or BROKER on regular.

3. Exotic Option  So Now What Financial Engineer Do is:  Create NON STANDARD PRODUCTS  Non standard products are those which do not have standard properties of derivatives.  These are traded OTC  These OTC derivatives are EXOTIC OPTION.

4. Types of ‘Exotic’ options  Bermudan  Barrier or Knock-in Knock-out  Cliquet or ratchet and reverse cliquets  Chooser  Digital/binary

5. Bermudan Options  These options are a special type of American-style option.  The holder has the right to exercise on defined dates over the life of the option.  These dates may coincide with the coupon payment dates. 0123 Exercise No exercise Possible In between these days

6. Barrier Options  Barrier Options are those option  whose Pay-Off depends on  whether the underlying asset price reaches a certain level  during the period of time.

7. Barrier Options  Barrier option can be classified as either: A. Knock-Out Options B. Knock- In Options  knock – out: Option ceases to exist when the underlying Asset Reaches a certain barrier.  Knock-In: Option comes into existence only when the underlying Asset reaches a Barrier.

8. Example: Knock- In PUT A knock-in put option with strike E = 4000 and barrier H = 3900, will only come in to existence when the index value of 3900 is hit. If it fails to hit the barrier there will be zero pay out even if the underlying (S) is below E at expiration (NB rebates may be paid in some cases) i.e Even if the option is ITM no exercise until barrier is reached.

9. Barriers Classification. Option PUT CALL IN: Exercise OUT: Don’t Exercise Below E.P (DOWN) Above E.P (UP) Price Barrier is

10. Barriers Classification CALLPUT UP & OUT UP & IN DOWN & OUT DOWN & IN

11. Pricing Barriers  Pricing is Based on B & S model.  So we shall deal the same in Next Class while studying B & S in detail.

12. Cliquet or Ratchet options  These instruments start out as normal call options with a fixed strike price.  But as time passes the strike is reset to be equal to the underlying asset.  This occurs on PRE-SPECIFIED dates.

13. Cliquet or Ratchet CALL DateIndex ValueS-EStrike Now40000 End of Period 141251254125 End of Period 243051804305 End of Period 341750 End of Period 439000-  Notice that the cliquet Call will pay out a total of 305 over the life span of the instrument.  A regular European-style Call option with a strike of 4000 and a life span of 4 periods would payout 0!

14. Pricing The Cliquet Ratchet options can be priced as a series of forward start (delayed start) options. Max (S t 1 – E,0) e r(T-t 1 ) + + Max (S t 2 – E,0) e r(T-t 2 )……. + Max (S t N – S N-1,0) FV of Cash Flows

15. Chooser Options  This instrument gives the holder the opportunity at some point in time ti,  for ti <= T,  to decide whether the option being held is a call or a put.  Pricing can be performed in a B&S framework.

16. Chooser Options  This instrument gives the holder the opportunity at some point in time ti,  for ti <= T,  to decide whether the option being held is a call or a put.  Pricing can be performed in a B&S framework.

17. Digital: Cash-or-nothing pay outs  A digital call option pays out a fixed sum (Q)  if the underlying finishes above the strike  and nothing if the underlying finishes at or below the strike. A.  In this type of structure the principal is guaranteed  but the final interest pay out is determined by  the path followed by the underlying reference index.