What Is an Option?
An option is a derivative contract that gives its buyer a right, but not an obligation, to transact in an underlying asset under specified terms. The option seller, or writer, receives a premium and takes on the corresponding obligation if the buyer exercises the option.
This asymmetry is what distinguishes options from forwards and futures. A forward commits both sides to the transaction. An option gives one side a choice and charges a premium for that flexibility.
Call Options
A call option gives the holder the right, but not the obligation, to buy the underlying asset at a predetermined price known as the strike price. In the formula below, \(K\) represents the strike price, while \(S_T\) represents the price of the underlying asset at expiration.
At expiration, the payoff of a long call is:
\[
\text{Payoff}_{\text{Long Call}} = \max(S_T-K,0)
\]
The call option has a positive payoff when \(S_T\) is greater than \(K\). In this case, the holder can exercise the option and buy the underlying asset at the strike price \(K\), which is lower than its current market price \(S_T\).
If \(S_T\) is equal to or lower than \(K\), exercising the right to buy at the strike price would not make economic sense. The option therefore expires worthless and its payoff is zero.
Put Options
A put option gives the holder the right, but not the obligation, to sell the underlying asset at a predetermined price known as the **strike price**. In the formula below, \(K\) represents the strike price, while \(S_T\) represents the price of the underlying asset at expiration.
At expiration, the payoff of a long put is:
\[
\text{Payoff}_{\text{Long Put}} = \max(K-S_T,0)
\]
The put option has a positive payoff when \(S_T\) is lower than \(K\). In this case, the holder has the right to sell the underlying asset at the strike price \(K\), which is higher than its current market price \(S_T\).
If \(S_T\) is equal to or greater than \(K\), exercising the right to sell at the strike price would not make economic sense. The option therefore expires worthless and its payoff is zero.
Strike Price and Expiration
The strike price is the contractual transaction price. Expiration is the date after which the option no longer exists. Options with different strikes and maturities on the same underlying can have very different prices and risk profiles.
Option Premium
The buyer pays the option premium to obtain the contractual right. The premium is the maximum initial loss for a long option position if the option expires worthless. For the seller, the premium is income received upfront, but the associated obligation can create much larger losses.
Moneyness
A call is in the money when the underlying price is above the strike and a put is in the money when the underlying is below the strike. At-the-money generally describes a strike close to the current underlying price. Out-of-the-money options have no intrinsic value at that moment.
American and European Exercise
European-style options can be exercised only at expiration, while American-style options can generally be exercised at any time up to expiration. The labels describe exercise rules, not geography. Exercise features can affect valuation, particularly for assets that pay dividends or other income.
Key Takeaways
Calls provide a right to buy and puts provide a right to sell. The strike, maturity, underlying price, volatility, interest rates and expected cash flows all influence option value. The buyer has limited downside equal to the premium, while the seller accepts an obligation in exchange for receiving that premium.
Previous: Futures Contracts Next: Option Payoffs