Options: call and put

[Jack]

Options are created by the market makers as a way to generate extra premiums. There are two types of options associated to a stock \(S_T\):

• the call option \(c(K,T)\): at time \(T\), the payout of a call option is \( (S_T - K)^+\);
• the put option \(c(K,T)\): at time \(T\), the payout of a put option is \( (K - S_T)^+\).

I have been wondering for a while how the trading of options moves the price of the underlying stock. Now it starts to make sense.

If the stock price goes above the strike price, then the option seller X will suffer a loss when the buyer Y exercises the option.
To hedge this potential loss, a simple way is to buy a number of shares of the underlying stock, which is determined by \(\Delta\).
If the seller sells a large amount of call options, then they would buy a proportionally large amount of shares to hedge the potential loss.
This will push the price higher.