I have the following question. Consider that you have a stock currently trading at 100\$. In one month it can jump to 120\$ with probability 99% and go to 80\$ with probability 1%. How much is call option with strike at 110$ worth now?
So when you do replication portfolio consisting of 0.25 stock and -20\$ gives exactly the same payoff as the option, hence the option should be worth 5\$. But again consider someone who wants to sell you security that in 99% cases gives you 10\$ and in remaining 1% gives you 0\$. How much would you be willing to pay for it? My whole intuition says it should be close to 10\$, but again replication tells 5\$.
Can someone comment on this? I feel really annoyed by this, as I tend to believe the replication model (because it replicates option with certainty), but it contradicts my intuition.