Options Trading Basics: Definitions, Payoffs, and Sensitivity Factors

Options and Futures Contracts Fundamentals

Options vs. Futures Contracts: Key Differences

• Option Buyer: Has the right, but not the obligation, to transact. The buyer can abandon the option if desired. The option premium paid is the maximum financial exposure.
• Futures Contract Buyer: Cannot abandon the contract. The buyer is obligated to transact, leading to theoretically unlimited exposure.

Types of Options

• European Options: Can be exercised only at the expiration date.
• American Options: Can be exercised at any time up to the expiration date.

Call Options Defined

A Call Option gives the holder the right, but not the obligation, to buy a given quantity of an asset on or before some time in the future, at prices agreed upon today (the strike price, $E$).

When exercising a call option, you “call in” the asset.

Call Option Payoff at Expiry

At expiry, an American call option is worth the same as a European option with the same characteristics.

• If the call is In-the-Money (ITM), its value is $S_T – E$ (where $S_T$ is the spot price at expiry).
• If the call is Out-of-the-Money (OTM), it is worthless.

Selling (Writing) Options

• The seller (or writer) of an option assumes an obligation to buy or sell the underlying asset if the option is exercised.
• The seller receives the option premium in exchange for taking on this obligation.

Put Options Defined

A Put Option gives the holder the right, but not the obligation, to sell a given quantity of an asset on or before some time in the future, at prices agreed upon today (the strike price, $E$).

When exercising a put, you “put” the asset to someone.

Put Option Payoff at Expiry

At expiry, an American put option is worth the same as a European option with the same characteristics.

• If the put is In-the-Money (ITM), its value is $E – S_T$.
• If the put is Out-of-the-Money (OTM), it is worthless.

The payoff $P$ is formally defined as: $P = \text{Max}[0, E – S_T]$.

Option Valuation Scenarios (Moneyness)

• In-the-Money (ITM): Exercising the option would result in a positive payoff.
• At-the-Money (ATM): Exercising the option would result in a zero payoff (i.e., strike price $E$ equals spot price $S$).
• Out-of-the-Money (OTM): Exercising the option would result in a negative payoff (meaning the option should not be exercised).

Option Sensitivity Factors (The Greeks)

The Greeks measure the sensitivity of the option value to changes in various market parameters.

• Delta: Sensitivity of the option value to changes in the price of the underlying asset. (Positive for calls, negative for puts).
• Gamma: Sensitivity of Delta to changes in the price of the underlying asset (second derivative). Gamma is typically highest when the spot price ($S$) is close to the strike price ($E$).
• Theta: Sensitivity of the option value to the passage of time. (This measures time decay, which usually reduces option value).
• Vega: Sensitivity of the option value to changes in the volatility of the underlying asset. (Positive: higher volatility generally means higher option value).
• Rho: Sensitivity of the option value to changes in the risk-free interest rate.