How Level I tests option payoffs, moneyness, time value, value drivers, put-call parity, and one-period option pricing logic.
Options are where many Level I candidates either gain easy points or lose them fast. The exam usually starts with payoff classification, then moves to moneyness and value drivers, and finally tests whether you understand how arbitrage links calls, puts, stock, and cash.
Candidates often miss options questions because they:
The stronger reader draws the payoff in words before calculating anything.
For a call option at expiration:
$$ \text{Call payoff} = \max(S_T - X, 0) $$
For a put option at expiration:
$$ \text{Put payoff} = \max(X - S_T, 0) $$
Profit for the option buyer adjusts for the premium paid. That is why a positive payoff does not automatically mean a positive profit.
| Position | What you want |
|---|---|
| Long call | Underlying price to rise |
| Short call | Underlying price to stay below or not rise too much above exercise price |
| Long put | Underlying price to fall |
| Short put | Underlying price to stay above or not fall too much below exercise price |
Level I frequently tests position direction before anything more advanced.
| Concept | Meaning | Common trap |
|---|---|---|
| Exercise value (intrinsic value) | Immediate economic gain from exercise | Treating it as the full option value before expiration |
| Moneyness | Whether the option is in, at, or out of the money | Confusing it with profitability after premium |
| Time value | Option value beyond current exercise value | Forgetting it falls as expiration approaches, all else equal |
A call is in the money when (S > X). A put is in the money when (S < X).
| Factor | Call value effect | Put value effect |
|---|---|---|
| Higher underlying price | Increases | Decreases |
| Higher exercise price | Decreases | Increases |
| Higher volatility | Usually increases | Usually increases |
| Longer time to expiration | Usually increases | Usually increases |
| Higher interest rates | Usually increases | Usually decreases |
These relationships are a favorite Level I testing pattern because they reward understanding over memorization.
For a European call and put on a non-dividend-paying stock with the same strike and expiration:
$$ C + \frac{X}{(1+r)^T} = P + S_0 $$
The equation matters because the two sides create equivalent expiration payoffs. If the pricing relationship breaks, arbitrage may exist.
In a one-period binomial model:
$$ C_0 = \frac{pC_u + (1-p)C_d}{1+r} $$
with risk-neutral probability
$$ p = \frac{(1+r)-d}{u-d} $$
The deeper point is that contingent claim pricing can be built from replicated payoffs and no-arbitrage, not only from intuition about expected price moves.
A candidate sees a call that is in the money and concludes the long holder must have a profit. That is incomplete. A stronger answer asks whether the intrinsic value exceeds the premium originally paid.
That is standard Level I design: payoff logic first, profit logic second.
Which change is most likely to increase the value of both a call option and a put option on the same underlying?
Best answer: Higher expected volatility, because optionality becomes more valuable when the range of possible outcomes widens.
Why: Level I likes value-driver questions because they reveal whether you understand the economics of optionality.