There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with "optionality" embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knock-out, knock-in, barrier options, lookback options, Asian options, and Bermudan options. Again, exotic options are typically for professional derivatives traders.
For example: A steel manufacturer importing coal from Australia currently and in order to reduce the volatility of changes in prices he always hedges the coal purchases on a 3 monthly forward contract where he agrees with the seller on day one of financial quarter to supply coal at defined price irrespective of price movements during quarter. So in this case, the contract is forward/future and buyer has an intention to buy the goods and no intention of making profit from price changes.
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So, call options are also much like insurance - you are paying for a contract that expires at a set time but allows you to purchase a security (like a stock) at a predetermined price (which won't go up even if the price of the stock on the market does). However, you will have to renew your option (typically on a weekly, monthly or quarterly basis). For this reason, options are always experiencing what's called time decay - meaning their value decays over time.