Barrier Option

[[email protected]]

Hi David,
Would you kindly answer my following question?

Which of the following option strategies can give the buyer an unlimited profit?
a. An American digital option
b. A European lookback call option
c. A European butterfly spread
d. An up-and-out with rebate barrier option

The answer is B.

My question is for d. When barrier option is in, does it perform like the regular call/put option so it can also give the buyer an unlimited profit?

 

[David Harper CFA FRM]

Hi ldcn, If the stock is increasing, the up-and-out only acts like a call for a limited time: until it reaches the barrier. Then it "knocks out" so the knock-out feature is what prevents it from having an unlimited profit (I agree with the answer). The rebate is the fixed payment (e.g., x% of intrinsic value) so it cannot contribute to unlimited profit.

Now, if instead this were an "up-and-in barrier call option" then, I think, the profit would be unlimited. I hope that helps, David

 

[[email protected]]

Thanks.
In d, it doesn't specify it's a call. What if it's an up-and-out with rebate barrier put option? Then it can give an unlimited profit, right?

 

[David Harper CFA FRM]

No, a put, unlike a call, is limited to a gain of (K) if the asset price moves to zero. So, even a down-and-in put has a limited payoff.
The question is smart that way, (b) refers to lookback call not lookback either/put. thanks, David

 

[[email protected]]

Oh, I forgot the maximum gain is the strike in put. Thanks!
In regards to the lookback put, I think its profit can be unlimited since its strike price can be floating, right?

 

[David Harper CFA FRM]

Oh, hey, right, i forgot about floating strike lookback put: I agree with you, seems like that payoff is technically unlimited, good point, thanks David

 

[jcjc0602]

What about a, what if it's a asset or nothing? The profit of that can be unlimited. Or there is only fixed payment for American style digital option.

 

[David Harper CFA FRM]

Oh, nice, I certainly did miss that myself (+ star for the nice observation) , what is everybody else's excuse ... where is this question from?

In any case, asset-or-nothing does appear to have an unlimited upside, as illustrated chart from Peter James' Option Theory. I agree with jcjc0602 because question says "which strategies ... can give buyer unlimited profit?"