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Option basics

1. What are stock options?

2. What is option premium?

3. Four basic profit and loss (P&L) calculations for option trading

    3.1 Long call options

    3.2 Long put options

    3.3 Short call options

    3.4 Short put options


1. What are stock options?

A stock option is a financial contract based on individual stocks that is traded on an exchange and settled by a clearing house. The contracts are divided into call options and put options. In addition, options can be divided into American options and European options according to the exercise method. The vast majority of US stocks and ETF options are American options, while index options are generally European options.

The buyer of an American call option has the right to buy the underlying stock at the strike price on or before the expiry date of the contract, and the seller of the call option is obliged to sell the underlying stock at the strike price if the option is exercised.

The buyer of an American put option has the right to sell the underlying stock at the strike price on or before the expiry date of the contract, and the seller of the put option is obliged to buythe underlying stock at the strike price if the option is exercised.

The definition of European option is similar to that of American option, except that the option can only be exercised on the expiry date of the contract.


2. What is option premium?

Option premium is the cost of an option or the price of an option transaction. The price of stock options traded on an exchange is displayed in a per-share-basis. The option seller charges premiums.


3. Four basic profit and loss (P&L) calculations for option trading

3.1 Long call options

The profit of buying a call option = (stock price - exercise price - option premium) * number of stocks; the maximum loss is the premium paid for the option.

Suppose a trader buys a call option at the market price of $10, and the strike price of the option is $90. On the expiration date, there are several possibilities:

1) If the price of the underlying stock is less than $90, the trader will choose not to exercise. The maximum loss is the cost of the option premium paid. P&L = -$1000;

2) If the price of the underlying stock is $90, if the trader chooses to exercise and buy 100 shares at $90, P&L = (stock price - exercise price - option premium) * number of shares = (90 - 90 - 10) *100 = -$1000; if the trader chooses not to exercise, P&L = -$1000;

3) If $90 <price of the underlying stock <$100 - for example, when the price of the underlying material is $95 - the trader chooses to exercise, P&L = (stock price - exercise price - option premium) * number of shares = (95 - 90-10) *100 = -$500

4) If $100 <price of the underlying stock - for example, when the price of the underlying material is $105 - the trader chooses to exercise, P&L = (stock price - exercise price - option premium) * number of shares = (105 -90-10 )*100 = $500


3.2 Long put options

The profit of buying a put option = (exercise price - stock price - option premium) * number of stocks; its maximum profit is the exercise price * number of stocks - the option premium, and the maximum loss is the premium paid for the option.


3.3 Short call options

The loss of a short call option = (stock price - exercise price - option premium) * the number of stocks, the maximum loss may be infinite; the maximum profit of a short call option is the option premium.

Suppose a trader sells short a call option at the market price of $10, and the strike price of the option is $90. On the expiration date: 

1) The price of the underlying stock is $105, and the trader is assigned on the exercise. P&L = (option premium - stock price + exercise price) * number of shares = (10 - 105 + 90) *100 = -$500; 

2) The price of the underlying stock is $95, and the trader is assigned on the exercise. P&L  = (option premium - stock price + exercise price) * number of stocks = (10 - 95 + 90) *100 = $500


3.4 Short put options

The loss of a short put option = (exercise price - stock price - option premium) * number of shares; the maximum profit of a short put option is the option premium.