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Option means that particular type of contract that gives the holder the right, but not the obligation, to buy or sell the security on which the option is registered, called the underlying instrument, at a specific strike price within a specific date, in exchange for a non-recoverable premium paid.
Options can have the most diverse underlyings: shares, commodities, interest rates. The fundamental difference between options and other derivative instruments consists in the holder's right of withdrawal: he is not obliged to purchase the underlying asset, but can do so if he derives actual economic benefit from it by exercising the option.
For this reason they are also called asymmetric derivative securities. Options give the right to call or put a security at a predetermined strike by a defined date. By buying call options or selling put options you can take bullish positions; vice versa, bearish positions can be taken by selling calls or buying puts.
An option is to all intents and purposes a contract that is stipulated between two market players: this contract is characterized by the underlying instrument, the duration of the contract, the strike exercise price and the premium paid for this contract.
The right to exercise the option can be either limited only to expiry, or extended to the entire time until expiry. Options are widely used for speculative purposes or as financial hedging in medium/high risk investments: for example, an importer can hedge/protect himself from exchange rate risk in the long term by subscribing to an option on the price of the imported goods if the purchase of the same is distant in time.
In fact, in the case of purchasing call options, the maximum possible loss is the premium paid plus the trading commissions due to the intermediary, while the profit is theoretically unlimited; vice versa, in the case of selling call options, the maximum profit is the premium paid by the buyer while the possible loss is unlimited.
In case of purchase of put options, which give the right to sell the underlying at the strike price, there is a maximum profit of the price itself minus the cost of the contract. Obviously, whether or not it is convenient for the buyer/seller to exercise the option at the end or within the time limits will essentially depend on the difference between the exercise price of the option or the strike price, initially stipulated in the option contract, and the final actual value of the underlying asset at maturity.
The more or less correct evaluation of the price of an option based on the current value of the underlying asset and the estimated future value then becomes crucial. In particular, the treatment of the option price is the subject of a vast mathematical literature within which, despite some intrinsic limitations, the Cox-Ross-Rubistein models and the Black and Scholes formula are particularly well-established.