The option writer’s purpose is to earn the premium paid by the option buyer.
The buyer pays a premium hoping that in the time before the option expires, the price of the underlying asset will move in the direction he has bet on.
The option writer has to take account of several factors in pricing the option including: the current price of the underlying asset, the historical volatility of the underlying asset and the value of time.
Time has a value – longer time frames are priced higher because it gives the underlying asset longer to reach the strike price, the price at which the buyer will be in-the-money.
Higher price volatility in the underlying asset also increases the premium the option writer will demand for an option. Assets prone to large price swings are more likely to move the buyer to an in-the-money position. Many options writers use the Black-Scholes model to price volatility, but the model is not universally loved.
The Black-Scholes formula has approached the status of holy writ in finance, and we use it when valuing our equity put options for financial statement purposes…
If the formula is applied to extended time periods, however, it can produce absurd results… Even so, we will continue to use Black-Scholes when we are estimating our financial-statement liability for long-term equity puts. The formula represents conventional wisdom and any substitute that I might offer would engender extreme skepticism.
Warren Buffett, Berkshire Hathaway Shareholder Letter, 2008.
The option writer’s objective is option pricing that’s both sufficiently attractive for investors to buy and sufficiently far from the strike price that the writer will make a profit because the option will expire without reaching the strike price.
For any option that expires without being exercised, the writer keeps the full premium paid for the option by the buyer.
If the option buyer exercises the option, the writer pays the difference between the exercise price and the market value. Options are generally only be exercised when they are in-the-money sufficiently to make a profit for the buyer after all costs have been taken into account. This is the case with American options. If the option writer writes European options, these can only be exercised at their expiry date. (The American/European terminology is purely historical and is not related to where these options can actually be traded.)