Define c the premium of an out of the money call option for the strike price k and the time to maturity t, where the stock price s < k. One executes the following strategy:
sell this call and get money c;
when t goes to 0, if s stays below k, do nothing;
if s rises up and beyond k, buy the stock at s = k;
if s drops down thereafter, sell the stock at s = k;
redo 3 and 4 if s moves across k multiple times until t = 0;
then one must have bought stock to be assigned if s > k;
otherwise the call is expired with no stock on hand.
When executing orders at a specific price point, there is an inherent trade-off between execution certainty and price precision. For instance, if you aim to transact at exactly $50:
Market Orders:
A market order ensures rapid execution, but due to slippage and market momentum, the fill price may deviate slightly, such as $50.1 or $49.9. This deviation prevents you from achieving the exact target price.
Limit Orders:
A limit order set at $50 guarantees that you will only execute at that price or better. However, if the market does not reach $50, the order may remain unfilled, leaving your position exposed to subsequent price movements.
