Options FX
b e e qua l t o the pr i c e o f the v ani l l a op t i on wi th the s ame s t r i ke . I t sho u l d now b e o b v i o us tha t the pr i c e s o f the kno c k- in and kno c k- o ut op t i ons a r e e xp e c t e d t o b e l owe r than the v ani l l a op t i on wi th the s ame s t r i ke . In th i s wa y, a p ur cha s e r o f an e xo t i c op t i on ma y s t r i v e e s s ent i a l l y t o g a in the s ame e xp o sur e t o a v ani l l a op t i on b ut a t a l owe r pr i c e - on the c ond i t i on tha t h i s pr e d i c t i on a b o ut whe the r the und e r l y ing wi l l r e a ch the b a r r i e r l e v e l ho l d s t r u e . Wh i l e the p ur cha s e r o f the e xo t i c op t i on d o e s g a in an e xp o sur e s imi l a r t o the v ani l l a op t i on, the pr i c ing d ynami c s d o chang e d r ama t i c a l l y. Wi th v ani l l a op t i ons , the pr i c e i s a lwa y s inc r e a s ing wi th r e sp e c t t o the vo l a t i l i t y
Figure 2. Reverse-knock-out call option. The green (blue) payoff line is if the barrier is (not) touched during the life of the option.
Figure 1. Knock-out call option. The green (blue) payoff line is if the barrier is (not) touched during the life of the option.
p a r ame t e r. Howe v e r , b a r r i e r op t i ons c an b eha v e qu i t e d i f f e r ent l y. Fo r e x amp l e , a r e v e r s e -kno c k- o ut c a l l op t i on wi th the und e r l y ing t r a d ing c l o s e t o the b a r r i e r wi l l d e c r e a s e in v a lu e f rom an inc r e a s e in vo l a t i l i t y a s the chanc e o f h i t t ing the b a r r i e r inc r e a s e s . On the o the r hand , the v a lu e o f the s ame op t i on wi l l inc r e a s e in v a lu e f rom an inc r e a s e in the vo l a t i l i t y, i f the und e r l y ing i s f a r f rom the b a r r i e r , a s the inc r e a s e d l i ke l iho o d o f h i t t ing the b a r r i e r i s c omp ens a t e d by the inc r e a s e d v a lu e o f the op t i on wi th r e sp e c t t o i t s s t r i ke . Th i s imp l i e s tha t s imp l e g amma s c a lp ing s t r a t e g i e s a s e xp l a in in pr e v i o us
a r t i c l e s , f o r
e x amp l e , b e c ome v e r y d i f f i c u l t t o mana g e , du e t o the c omp l e x inf lu enc e
o f b o th the s t r i ke and the b a r r i e r on the d e l t a o f the op t i on . The r e f o r e , kno c k- in, kno c k- o ut , r e v e r s e - kno c k- in, and r e v e r s e - kno c k- o ut ’s a r e o f t en b e s t su i t e d a s d i r e c t i ona l op t i on t r a d e s , a s d e s c r i b e d in the a r t i c l e a b o ut sp e c u l a t i v e t r a d ing . Ano the r c l a s s o f e xo t i c s op t i ons a r e the Ame r i c an d i g i t a l s a l s o known a s t o u ch op t i ons . The y f unc t i on l i ke b e t s by p a y ing a pr e d e t e rmine d amo unt i f a c e r t a in c ond i t i on i s me t . The p a y o f f i s thus the f u l l amo unt o r no th ing , wh i ch g i v e s r i s e t o the t e rm d i g i t a l . The one - t o u ch op t i on p a y s o ut i f the pr i c e o f the und e r l y ing t o u che s the b a r r i e r b e f o r e e xp i r y ( s e e Fi g ur e 5 ) . The no - t o u ch op t i on wo rk s the o the r wa y a ro und and
Figure 3. Knock-in call option. The green (blue) payoff line is if the barrier is (not) touched during the life of the option.
FX TRADER MAGAZINE July - September 2010 45
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