[wdpk]

>Taleb's big argument here is that Bitcoin will someday be obsolete and will have a value of 0. Since Bitcoin doesn't generate income or pay dividends, its present value is thus 0. That's a strange position for an options trader to take. Options, by their nature, expire, and have a value of 0 at some future time. Yet they are traded during their life as having value.

this remark is not true, only some possible paths of an option end-up at 0 otherwise nobody would take the other side of the bet... In the parlance of Options trading, there will be options that end-up at expiry in the money with a strictly positive payoff and some out of the money. In order to price an option expiring sometime in the future as of today, you have to take into account all the possible future payoffs (in and out of the money), and the probability distributions of such payoffs then propagate back to present time (check tree methods or cox ross rubinstein for an example of how this can be done). So if all possible future payoffs were 0 then the present value of the option would be 0 too. Same thing with bitcoin, if in the future you think with 100% probability that the price will be 0 (the absorbing barrier) then going backward from that future moment, you'll get the "rational" price at t-1 to be 0 and so on until today.

[Animats]

Technically, when an option expires, its value goes to zero. However, normally you don't let an option in the money expire; you exercise it first. Some brokers do that for you at expiration.

[wdpk]

Technically speaking, as you get closer to maturity, the "time value" of the option goes down towards 0 but options also have intrinsic value and the total value of the option converges to it's intrinsic value not to 0 (intrinsic value can be 0 but not only). Now if you do not exercise your in the money option it's like having a winning lottery ticket and not cashing it, it's not something a rational agent would do.