Subject:

A **call option** is the right (but not obligation) to buy the underlying for a specified price (strike price K), on a specified date (expiry).

If the underlying fails to rise above the strike price before expiration, then the call expires worthless as it would be cheaper to buy the underlying directly from the market. As there is no upper bound on the price of the underlying, the potential profit of a call is theoretically unlimited.

Let's consider how a call option works.

Say that the stock A is currently priced at $10.

You believe that it will rise over the next month, so you buy the call option on the $11 strike expiring in a month for $1.

**Scenario 1.** If the stock is worth $15 on expiration, then you can exercise the call option and buy the stock at the strike price of $11. You close out your position by selling the stock in the market for $15, which is a gain of $15−$11=$4.

Accounting for the initial cost of the option, your net profit is $4−$1=$3.

**Scenario 2.** If, however, the stock were to drop in value to $8, then it is pointless to exercise the call option. As such, all that you have lost is the initial cost (premium) of the option, so your net profit is −$1.

The payoffs (net profit) of this trade when the stock expires at different values is summarized in the following graph:

**Trading Call Options**

Even though the option value will increase as the stock price increases, it is not necessarily profitable to buy calls even though you believe that the stock price will increase, unless the extent of increase is large enough to compensate for the theta that you are paying.

For example, consider the case where the underlying is trading at $100, and (all that you do is) you buy the $110 strike for $2. Then you will need the underlying to be above $112 on expiration, in order for you to have profited on this trade.

Furthermore, in the stock market, option volatility often decreases as the stock price increases, as it reflects investor confidence in the company.

## Options Trading Math 101

Hence, buying upside calls when the stock goes up could still lose you money on vega and theta.

Consider buying calls in the following situations:

- You believe that the underlying will move up more than the implied volatility.
- You believe that the underlying will move up and that volatility will increase.
- You believe that the underlying will move up more than the cost of theta.

Consider selling calls in the following situations:

- You believe that the underlying will move down.
- You strongly believe that the underlying will not move up significantly.

**Greeks of Call Options**

The greeks of a call option are as follows:

- Long Delta
- Long Gamma
- Long Vega
- Paying Theta
- Long Rho

There are explained in detail in the corresponding pages about the Greeks.

Call up the exchange Buy the stock Sell the stock Sell the Call on the $90 strike Sell the Put on the $90 strike Buy the Put on the $90 strike that expires in 1 month Nothing

You are long the Jan Call on the $90 strike.

On expiration, the stock closed at $100.

When the trade settles, what do you need to do so that you will no longer have a position?