The quick answer is yes and no. It all depends on where the option is traded. An option contract is an agreement between the buyer and the seller of the contract to buy or sell an underlying asset at a certain price, amount and time. These are referred to as the strike price, the contract size and the expiration date, respectively. Options are sold in two places: on option exchanges and over the counter.
Option exchanges are similar to stock exchanges in that trade happens through a regulated organization, such as the Chicago Board Option Exchange (CBOE). Exchange-traded options at the basic level are standardized; this means that each option has a set standard underlying asset, quantity per contract, price scale and expiration date. For example, when looking at a May05 MSFT 30.00 call option, the CBOE has standardized that each option contract represents 100 shares of MSFT common shares, the strike price is $30, and the contract expires on the third Friday of May. There is no customization at the basic level of option exchanges, and the terms of the contract are set out by the exchange.
Flexible exchange options (FLEX) allow for customization of the contract specifics of exchange-traded options; they are most often written by a clearing house. There are also exchange-specified rules that must be followed when creating a FLEX option; for example, the exercise date must differ from the exercise date of all other options and there may be a minimum size. This allows for some customization, which means an option contract writer can change some of the details of the contract.
Over the Counter
Options are also traded in the over-the-counter option market. Over-the-counter options are traded through a wide network of various brokers and dealers. This market allows for the complete customization of option terms, from the strike price to the expiration date. The price that is paid or received for the option is dependent on the price someone in the market is willing to sell for or pay, and this is determined by the terms of the option.
However, there is more risk in the over-the-counter market than in the exchange-traded market. In the over-the-counter market, the other party to the contract may not hold up his or her side of the agreement. This is unlike exchange-traded options, which are guaranteed by the clearing corporation to be exercisable, no matter what the other party to the option does.
For more information on options, please read the Options Tutorial.