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 European Reverse Knock Out Option Replication
Issued on September 26 2011 par European Reverse Knock Out Option Replication
Barrier options are almost exclusively OTC (Over The Counter ) products. Replication with vanilla options is sometimes a better deal.
Barrier options, sometimes called Knock In or Knock Out, exibit a lot of advantages, mainly because they are cheaper as vanilla options.
They are extensively traded on OTC markets. I - Reverse Knock Out Barrier Options Amongst barrier options are 'Reverse Knock Out', 'In the Money' option which expire worthless if the asset reaches a level called the barrier. An up and out call is a call with a barrier beyond the strike, a down and out put is a put with a barrier under its strike. For example, a 100 call 120 KO is a call that expires worthless if the underlying reached the level 120 once before expiry. a - Advantages Because the upside of the payoff is limited, they are cheaper than vanillas. b - Disadvantages As far as there is a barrier, it can be knocked. II - Replication Replicating barrier options is the way one can reach the same payoff using vanilla products. a - Reverse KO Break Down A reverse KO call with strike K and the barrier set at the level H is something alike as long call spread struck at K and H, and a number n of short tight call spreads with strikes H and H+x. The number n is equal to (H-K)/(x). For example, if one wants to replicate a 100 call KO 120, it can be done using the strikes 100,120 and 121: → 1 long call spread 100/120 → 20 short call spreads 120/121 (x=(120-100)/1=20/1=20) If the asset reaches 120 at expiry one is left with the same payoff is if he was long the 100 call. If the asset reaches 121 or above at maturity, the whole portfolio expires worthless. One can be more precise using the strike 100/120/120.5 A 100 call KO 120 can be replicated with : → 1 long call spread 100/120 → 40 short call spreads 120/120.5 (x=(120-100)/0.5=20/0.5=40) ■ If the asset reaches 120 at expiry one is left with the same payoff is if he was long the 100 call. ■ If the asset reaches 120.5 or above at matiruty, the whole portfolio expires worthless. ■ An interesting point is that using european options make the "barrier" only set at expiry. The underlying can reach levels beyond, before expiry, without knocking the portfolio out. b - European 100 call KO 120  Previous : Ratio Backspreads - Delta Neutral European Reverse Knock Out Option Replication |
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