In this article I am explaining you the call option by giving you an example.

Buy a Call:

It is expected by the buyer that the price may go above his chosen ‘strike price’. A premium is being paid by him that will never be refunded, and he possess the right to exercise the option at the strike price, what it means is that he can choose to buy the stock at the strike price. If the price goes up enough as anticipated by the buyer then the buyer pays the strike price to actually purchase the stock. After purchasing, he can then choose to either hold the stock, or sell it to realize his profit.

Write a Call:

The premium is received by the writer. If it is decided by the buyer that he will exercise the option, then the writer has the obligation to sell the stock at the strike price. If the buyer does not exercise the option, then the writer still gains profits in the amount of the premium.

• ‘Trader A’ (Call Buyer) have purchased a Call contract in order to buy 100 shares of XYZ Corp from ‘Trader B’ (Call Writer) at $50_/share. The current price is $45_/share, and premium of $5_/share is being paid by ‘Trader A’ pays. If right before expiration the share price of XYZ stock rises to $60_/share , then ‘Trader A’ is now able to exercise the call by buying 100 shares for $5,000 from ‘Trader B’ and sell them at $6,000 in the stock market.

Trader A’s total earnings (S) can be calculated at $500. Sale of 100 stock at $60 = $6,000 (P) Amount that is paid by him to ‘Trader B’ for the 100 stock bought at strike price of $50 = $5,000 (Q) Call Option premium that he pays to Trader B for buying the contract of 100 shares @ $5_/share, excluding commissions = $500 (R)

S=P-(Q+R)=$6,000−($5,000+$500)=$500′

• However, if in case the price of XYZ drops to $40_/share i.e. below the strike price, then ‘Trader A’ would not exercise the option. (Why he should buy a stock from ‘Trader B’ at 50, the strike price, when it can be bought at $40 in the stock market?) So in this case Trader A’s option would be worthless and the whole investment, i.e. the fee (premium) for the option contract, $500 (5_/share, 100 shares per contract) would be lost. Total loss of Trader A is limited to the cost of the call premium in addition to this the sales commission to buy it.

It has been illustrated by this example that a call option has positive monetary value when the underlying instrument posses a spot price (S) that is above the strike price (K). Since unless the option is “in-the-money it will not be exercised, so the payoff for a call option is

max[(S − K);0] or, more formally to be written as, (S − K) ⁺

Prior to exercise, the option value, and therefore price, shows variations with the underlying price and with time. The “likelihood” or chance of the option “finishing in-the-money” must be reflected by the call price. Thus the price should be higher having more time to expire (except in cases when a significant dividend is present) and also it should be having a more volatile underlying instrument. The science of determining this value is the central tenet of financial mathematics. The the Black-Scholes formula is the most common method that can be used. Whatever the formula used, it is necessary that the buyer and seller must agree on the initial value (the premium), otherwise the exchange (buy/sell) of the option will not occur.

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