A call option, often simply labeled a "call", is a contract, between the buyer and the seller of the call option, to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at a certain time (the expiration date) for a certain price (the strike price). The seller (or "writer") is obligated to sell the commodity or financial instrument to the buyer if the buyer so decides. The buyer pays a fee (called a premium) for this right. The term "call" comes from the fact that the owner has the right to "call the stock away" from the seller.
Option values vary with the value of the underlying instrument over time. The price of the call contract must act as a proxy response for the valuation of (1) the estimated time value -- thought of as the likelihood of the call finishing in-the-money and (2) the intrinsic value of the option, defined as the difference between the strike price and the market value multiplied by 100(max[S-X, 0]). The call contract price generally will be higher when the contract has more time to expire (except in cases when a significant dividend is present) and when the underlying financial instrument shows more volatility. Determining this value is one of the central functions of financial mathematics. The most common method used is the Black-Scholes formula. Importantly, the Black-Scholes formula provides an estimate of the price of European-style options.
Whatever the formula used, the buyer and seller must agree on the initial value (the premium or price of the call contract), otherwise the exchange (buy/sell) of the call will not take place.
Adjustment to Call Option: When a call has the strike price above the break even limit, i.e. when the buyer is making profit, there are many avenues to explore. Some of them are as follows:
Similarly, if the buyer is making loss on his or her position i.e. the call is out-of-the-money, where the market price is less than or equal to the exercise price. The buyer can make several adjustments to limit the loss or even make some profit.