So if i want to price an option I can't simply discount the future cashflows to the present value (like i do it with bonds) because I don't have the certainty to get something out of it. So to price the Option i look at how much it would cost me to hedge it by creating a replication portfolio with stocks and bonds and selling it. When i sell this replication portfolio i get no return because I am perfectly hedged. I only get the risk free rate on my invested capital (price of the option) because of BS: Ke^-rt so i get the risk free rate by not paying for the actual strike but on a discounted version of it. is my intuition right here?Can someone tell me if I'm missing something.
Posted by True_Ad520
1 Comment
the risk free rate is a cost when investing in options (long) this is because it is basically a cost you pay to the market maker when they delta hedge their position (they need to borrow cash in the market, to hedge)
so that r included in B/S is not a net benefit to you as the option buyer. you compare the premiums over time to the cost of hedging for the remaining duration of the option contract.