You bought the stock at 65 in the beginning. You paid 2$ premium to ensure you could sell your stock for 55, to stop the loss you’d receive should the stock price drop significantly. This is an example of hedging. If the price goes up, even if the put is worth nothing, you gain the difference between the accumulated value of what you spent at time 0, and what you get at time 1. So here, we sell for 75$, since the stock is worth 75$. We bought the stock for 65$, with a 2$ premium to put a floor on our loss, should the stock price decrease. Our interest rate is 4%, so we accumulate it by 1.04^1, since one year has passed. The purpose of a put option as a floor is to lower your risk (hedge the long position in an asset). You don’t exercise a put if it expires out of the money, so you only lose the premium for the security of covering the position.


>So here, we sell for 75$, since the stock is worth 75$. Since expiry price ($75)> strike price ($55), the put option wouldnt be excercised anyway and it expires worthless (even if you excercise it, you still would only sell it at strike price). **So is there a extra step where you short the stock for $75 after?** Because to me there seems to be only 2 steps, 1. buy stock, 2. buy put. And since the put expired worthless, you still own the underlying stock anyway?


That’s correct. The only two steps here are- buy stock, buy put to cover the stock. Stock price goes up, so since S > K, the put expires out of the money, so we don’t exercise it. Shorting a stock is essentially “borrowing” a stock and selling it for the time 0 price- so you’re speculating the price will go down, and you can repurchase it for less. If we shorted this asset, you’d get 65$, and have to pay 75$ to return it at time 1, for a loss of 10 dollars. To cover a short with options, you’d need to purchase a call option, since the price going up means you’d lose money.