9.3 Option Payoffs, Moneyness, and Risk
Key Takeaways
- A call gives the holder the right to buy the underlying, while a put gives the holder the right to sell the underlying.
- Option buyers have limited loss equal to the premium paid, while option sellers can face large losses depending on the position.
- Moneyness compares the underlying price with the exercise price and helps describe intrinsic value.
- Option value depends on intrinsic value, time to expiration, volatility, interest rates, income on the underlying, and exercise terms.
- Protective puts, covered calls, and basic long calls or puts create distinct payoff profiles that CFA candidates should recognize.
Option contract rights
An option gives its buyer a right and its seller an obligation. A call option gives the buyer the right to buy the underlying at the exercise price. A put option gives the buyer the right to sell the underlying at the exercise price. The buyer pays a premium for this right.
The seller, also called the writer, receives the premium and takes the other side. A call writer may have to sell the underlying at the exercise price. A put writer may have to buy the underlying at the exercise price. The premium is compensation for accepting that obligation.
American-style options can be exercised any time up to expiration. European-style options can be exercised only at expiration. Level I questions often focus on expiration payoffs, where exercise style usually affects value less than the basic payoff formula.
Payoff and profit
Payoff is the value received from the option at exercise or expiration. Profit subtracts the premium paid or adds the premium received. This distinction prevents many exam errors.
For a call, payoff at expiration is the greater of zero and spot price minus exercise price. For a put, payoff at expiration is the greater of zero and exercise price minus spot price. The option buyer then subtracts the premium to find profit.
| Position | Expiration payoff | Maximum loss for buyer | General use |
|---|---|---|---|
| Long call | max(0, S - X) | Premium paid | Upside exposure |
| Short call | -max(0, S - X) | Potentially large | Income or covered sale strategy |
| Long put | max(0, X - S) | Premium paid | Downside protection or bearish view |
| Short put | -max(0, X - S) | Large if underlying falls | Income or willingness to buy |
If a call has exercise price 50 and the underlying is 58 at expiration, the call payoff is 8. If the premium was 3, the buyer's profit is 5. If the underlying is 47, the payoff is zero and the buyer loses the 3 premium.
Moneyness
Moneyness describes the relationship between the underlying price and exercise price. A call is in the money when the underlying price is above the exercise price. A put is in the money when the underlying price is below the exercise price.
An option is at the money when the underlying price is approximately equal to the exercise price. It is out of the money when immediate exercise would produce no positive payoff. Out-of-the-money options can still have value because future price movement may make them profitable.
| Option | In the money | At the money | Out of the money |
|---|---|---|---|
| Call | S > X | S = X | S < X |
| Put | S < X | S = X | S > X |
Intrinsic value is the value from immediate exercise. Time value is the option value beyond intrinsic value. Time value reflects the chance that favorable price movement can occur before expiration. Higher expected volatility generally increases option value because the buyer benefits from favorable movement while downside is limited to the premium.
Common option strategies
A protective put combines a long underlying position with a long put. It preserves upside above the underlying price while limiting downside below the exercise price, after considering the premium. It is like buying insurance on a stock position.
A covered call combines a long underlying position with a short call. The investor receives premium income but gives up upside beyond the call exercise price. This strategy may fit a neutral to mildly bullish view, but it does not protect heavily against a large decline.
A long call offers leveraged upside with limited loss. A long put offers downside exposure or protection with limited loss. Short option positions collect premium but transfer favorable optionality to the buyer.
Structured aid: option question workflow
- Identify call or put.
- Identify long or short.
- Compare spot price with exercise price to classify moneyness.
- Calculate payoff at expiration.
- Adjust for premium to calculate profit.
- Link the payoff shape to the investor's objective.
Exam focus
When the question asks for payoff, ignore the premium unless the stem asks for profit. When the question asks for profit, include the premium. When the question asks for moneyness, compare spot and exercise price from the option holder's perspective.
The most common conceptual trap is assuming option buyers have unlimited losses. They do not. A buyer can walk away from exercise and lose only the premium paid. Option sellers have received the premium but may face much larger adverse price movement.
A call option with an exercise price of 60 expires when the underlying price is 68. The call payoff is closest to:
A put option is in the money when:
A covered call position is most accurately described as owning the underlying asset and: