June 18th, 2015, 12:58 pm
Suppose the underlying now is 70, once itreaches 100, the option?s pay off is 1. This option never expires and assumesinterest rate is 0.I think one can hedge this option byholding 0.01 share of this underlying, once it reaches 100, then earn (100-70)*0.01=0.3.So the price of this option should be 1-0.3=0.7.On the other hand, the underlying hits 100almost surely, so it will pay off with probability 1. And it payoff is 1, so itseems its price should be 1 too. Then what?s wrong with this argument?