Most indexes use European options, they can be exercised only on the day of expiration. No shares will change hands during the settlement period for European-style options and is all done on a cash basis (Financial settlement).
Assume the settlement price of SPX is $4010
If you are the owner of a call option Strike 4000, you would receive:
($4010.00 – $4000.00) X 100 = $1,000 The seller of that call option would pay you $1,000
If these were puts, the owner would receive nothing and would be out the premium paid for this contract.
The seller of the put pays nothing but will keep the premium they received.
Assume the settlement price of SPX is $4010
If you are the owner of a Put option Strike 4020, you would receive:
($4020.00 – $4010.00) X 100 = $1,000 The seller of that Put option would pay you $1,000
Investors can sell a European option contract back to the market before expiry and receive the net difference between the premiums earned and paid initially