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Stock options are simply contracts that confer the right, but not the obligation, to purchase or sell shares (typically 100 of them) at a specified "strike" price up to a specified "expiration time.  A contract to sell shares is called a "put" and one to buy them is referred to as "call".  If the price of the "underlying" stock that the option refers to is above the strike when the contract "expires" they will automatically be "exercised" so that the specified transaction occurs, assuming the buyer of the option (the one who got the right) has sufficient capital.  Note that for American options exercise can happen before the expiration date, whereas with European ones it can only happen at the point of expiration. 

In modern markets, there is abundant evidence that options typically control or at least guide the price of the underlying equity.  Early recognition of this in the 1990s is one of the factors that allowed me to transition to full-time investing, and it is still common for notes in my service to incorporate "premium" and "open interest" data from an options chain when attempting to predict short term pricing trends, and assess market sentiment on an equity.  The premium (compensation beyond the difference between current stock and strike prices) varies with the volatility (beta) of the stock, and the length of time to expiration (theta), with around 1% of the position value per week being a simplistic normal baseline.  Open interest is simply the number of contracts that are actually in existence for any given underlying, strike and expiration.  Note that this can be and frequently is less than the volume traded, which should you tell you something about options, market fundamentals, and available capital.

I have since gone on to analyze the long term effects of differing option setups on equity prices, but have only hinted at some of the details of my findings, since there has not yet been public recognition of these effects.