Combinations are trades constructed with both a call and a put. There is a special type of combination known as a “synthetic.” The point of a synthetic is to create an options position that behaves like an underlying asset, but without actually controlling the asset. Why not just buy the stock? Maybe some legal or regulatory reason restricts you from owning it. But you may be allowed to create a synthetic position using options.
What if, instead of a home, your asset was a stock or index investment? Similarly, if an investor wants insurance on his/her S&P 500 index portfolio, they can purchase put options. An investor may fear that a bear market is near and may be unwilling to lose more than 10% of their long position in the S&P 500 index. If the S&P 500 is currently trading at $2500, he/she can purchase a put option giving the right to sell the index at $2250, for example, at any point in the next two years.
In terms of valuing option contracts, it is essentially all about determining the probabilities of future price events. The more likely something is to occur, the more expensive an option would be that profits from that event. For instance, a call value goes up as the stock (underlying) goes up. This is the key to understanding the relative value of options.
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Speculation is a wager on future price direction. A speculator might think the price of a stock will go up, perhaps based on fundamental analysis or technical analysis. A speculator might buy the stock or buy a call option on the stock. Speculating with a call option—instead of buying the stock outright—is attractive to some traders since options provide leverage. An out-of-the-money call option may only cost a few dollars or even cents compared to the full price of a $100 stock.

The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset. 
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