Are Option Sellers "Cheated"?

Quote from Random.Capital:

Assume for the moment that we know how to price an arbitrary binary option. Can't we view a vanilla option as a collection of (hypothetical) binary options at different strikes, with different payoffs? Payoff would then be an integration along the strike price axis, from 0 to Price@Expiry.

Thinking out loud here...a perfect hedge for a binary with strike $X and a payout of $1.00 could be made with a call spread at $X and $X + $0.01. The price of that spread should equal the price of the binary divided by 100 ($1 = 100*$0.01).

Anyway, I'm meandering now...and looking forward to a possible SuperClassico Ultra-Retro Germany-Holland rematch in the final. :)
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You can't replicate the convexity, even at penny strikes, but you can get close. Empirically, it's been done to replicate lookback exotics with a touch option strip.
 
Quote from Random.Capital:
Assume for the moment that we know how to price an arbitrary binary option. Can't we view a vanilla option as a collection of (hypothetical) binary options at different strikes, with different payoffs? Payoff would then be an integration along the strike price axis, from 0 to Price@Expiry.

Thinking out loud here...a perfect hedge for a binary with strike $X and a payout of $1.00 could be made with a call spread at $X and $X + $0.01. The price of that spread should equal the price of the binary divided by 100 ($1 = 100*$0.01).

Anyway, I'm meandering now...and looking forward to a possible SuperClassico Ultra-Retro Germany-Holland rematch in the final. :)
More...
As atticus mentioned, I don't think either of the two will give you perfect replication, but, you're absolutely right, these methods can be and are used in practice. In the world of rates, various CMS exotics, digital and otherwise, are normally handled by replication with a portfolio of vanilla options. As I understand it, the same is true for all the dodgy FX exotics.
 
Quote from Random.Capital:


Anyway, I'm meandering now...and looking forward to a possible SuperClassico Ultra-Retro Germany-Holland rematch in the final. :)
More...

The real hurdle between Germany and the cup is Spain. I would not be surprised if the spaniards pull a win. Netherlands have not been really tested so far, but among the four remaining teams I think they have the highest chance to be the final match. Among the remaining teams, I like Holland because I find their soccer to be tactical, yet entertaining. The germans and spaniards is maybe too tactical.

Does anyone know sites where I can watch the matches live?

Back to options, you guys made good comments. Would comment/ask questions later. Enjoy the weekend.
 
Quote from tradingjournals:

The real hurdle between Germany and the cup is Spain. I would not be surprised if the spaniards pull a win.
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I really hope not... This Spanish team plays ugly footbal, IMHO. The Dutch are OK, but I don't think either of the two are a match for the mighty German machine.
 
Quote from Martinghoul:

I really hope not... This Spanish team plays ugly footbal, IMHO. The Dutch are OK, but I don't think either of the two are a match for the mighty German machine.
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You forgot Spain defeated Germany in the Euro 2008 final match. I think Spain plays more beautiful passing/possession football, and are quite pleasing in the middle. The strength of the Germans is their youth / ability to play mass attack and mass defense. Its amazing to see how dangerous they are on the counter. Whatever, it promises to be an exciting match.
 
Quote from neke:
You forgot Spain defeated Germany in the Euro 2008 final match. I think Spain plays more beautiful passing/possession football, and are quite pleasing in the middle. The strength of the Germans is their youth / ability to play mass attack and mass defense. Its amazing to see how dangerous they are on the counter. Whatever, it promises to be an exciting match.
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I have not forgotten. Those were dark times for me, as I was really hoping Russia would make it all the way to the final. Somehow, I just remember the 2008 Spanish team playing much nicer football than this one. I know it's mostly the same team and the same players, so must be just a subjective thing. But, I agree, Germans are young, fast and they seem so well-organized.
 
Quote from neke:

The strength of the Germans is their...ability to play mass attack and mass defense.
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Er, you're talking about football, right? :p
 
Quote from tradingjournals:

The real hurdle between Germany and the cup is Spain. I would not be surprised if the spaniards pull a win. Netherlands have not been really tested so far, but among the four remaining teams I think they have the highest chance to be the final match. Among the remaining teams, I like Holland because I find their soccer to be tactical, yet entertaining. The germans and spaniards is maybe too tactical.

Does anyone know sites where I can watch the matches live?

Back to options, you guys made good comments. Would comment/ask questions later. Enjoy the weekend.
More...

I should have bought options on my forecasting--seriously do they have options on soccer games :)
 
Quote from Random.Capital:

Assume for the moment that we know how to price an arbitrary binary option. Can't we view a vanilla option as a collection of (hypothetical) binary options at different strikes, with different payoffs? Payoff would then be an integration along the strike price axis, from 0 to Price@Expiry.

Thinking out loud here...a perfect hedge for a binary with strike $X and a payout of $1.00 could be made with a call spread at $X and $X + $0.01. The price of that spread should equal the price of the binary divided by 100 ($1 = 100*$0.01).

Anyway, I'm meandering now...and looking forward to a possible SuperClassico Ultra-Retro Germany-Holland rematch in the final. :)
More...

1. If the use your interpretation for ATM strike, it become easier to understand why a binary call option (European) is worth less than 0.50.

2. Do you think that Vanilla option is not: long one AON, and short K binary calls?
 
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