An option is a one-sided bet. The buyer pays a premium today for the right (not the obligation) to transact later. Pricing splits that premium into two pieces: what the option is worth if exercised now, and what the right to wait is worth.
Let S be the spot price of the underlying and X the exercise (strike) price. The exercise value is what the holder would receive by exercising immediately, floored at zero because the holder can always walk away.
Moneyness describes the sign of the exercise value:
- In-the-money (ITM): exercise value is positive. Call ITM when S > X. Put ITM when S < X.
- At-the-money (ATM): S ≈ X. Exercise value is zero or near zero.
- Out-of-the-money (OTM): exercise value is zero. Call OTM when S < X. Put OTM when S > X.
KEY: Exercise value never goes negative. The option holder is never forced to exercise at a loss.
Common mistakes
- Forgetting the zero floor. Exercise value cannot go negative. Trap: writing exercise value as S − X = −$3 for an OTM call. Correct answer is $0.
- Confusing exercise value with option premium. Premium = exercise value + time value. An OTM option has zero exercise value but a positive premium. Trap: "OTM call has zero value." False unless expiration is today.
- Reversing the volatility effect on puts. Higher σ raises BOTH calls and puts. Trap: "higher volatility raises calls and lowers puts." Wrong. The payoff floor at zero makes both directional bets gain from wider distributions.
Bottom line
- Exercise (intrinsic) value = max(0, S−X) for calls, max(0, X−S) for puts. Never negative; the zero floor always applies.
- Option premium = exercise value + time value. Time value is usually positive (a deep in-the-money European put can show a negative one) and goes to zero at expiration.
- Moneyness: ITM = positive exercise value, ATM = S ≈ X, OTM = zero exercise value (but still a positive premium before expiry).
- Six factors drive option value: S, X, r, T, σ, and cash flows on the underlying.
Exam shortcut
For exercise value: write max(0, S−X) for calls and reverse for puts. Never let the answer go negative. For factor signs, memorize "SXRT-σD": for calls the signs are +, −, +, +, +, −; puts flip every sign except T and σ (more volatility raises both, and more time usually does). For the arbitrage-versus-replication question: linear payoff = arbitrage (forwards, futures, swaps), kinked payoff = replication (options, contingent claims).
The full lesson (about 2,608 words, 17 min read) adds 5 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- pricing and valuation of options
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