Quote from HedgefundTrader2:
No one can decipher your meaningless statement. Good luck
I think that you are not right on this one. Atticus is using actual option terminology (the language is not common even to people who trade "more common" options, which are called vanilla options as opposed to exotic options. Binary range options/bets, touch/etc options, and vanilla options (the one that any option trader knows about) actually do exist. Just take some time to learn about them. Once you learn options and become profitable, you would most likely never revert back to stocks.
His logic is also very sound. I think (but not sure) that what he is saying is that one can get free money exploiting two ways to look the european binary range bet which pays depending on the outcome at expiration. In this case, a bet is placed and if the underlying is on the outside range, the better gets 100 for each bet placed.
What I understand him saying is that he wants to hedge this bet by building an opposite transaction which rests on this: instead of linking the position to the expiration date T, what if one looks at an interval of expirations taking place in interval [T-Epsilon, T] where Epsilon will be taken very small?
There are possible price paths that will lie in interval [T-Epsilon, T[, where the latter "[" means the last instant is excluded. Therefore if one tried to approximate the price the binary range bet by pricing it as a time-dependent position corresponding to interval [T-Epsilon, T], one should then allocate a premimum reflecting possible paths that will lie in interval [T-Epsilon, T[. This should be true for any positive small Epsilon (as small as you wish but positive).
What I think is very interesting is that even if Epsilon was to tend towards zero, I think that the american pricing (involing interval [T-Epsilon, T]) may not converge to the european pricing. I have not looked at the maths of this, but my sense is that there is a discontinuity at time T between the limit of the american value (which will be higher) and the european value (which would be lower).
In practice I would say that one can choose an Epsilon small enough, but in theory even the smallest of all epsilons would not make that gap disappear. If this is the case, there is no way one can remove this arbitrage as long as there are european and american instruments based on this modeling and can implement it. In other words, if models are used, there is discontinuity and no one can do a damn about it!
I would send a note to Atticus if I were you,and go back to good terms. The least we can say is that he is not selfish as he is sharing very worthy information. Let us not attack personalities.
The other lesson that one can take away is to grasp the crux of the idea, and implement it elsewhere. The european/american thing is a goldmine. I have various plays myself that rest on it in equities.
