A call option with strike price $50 on a stock currently trading at $60 has a market price of $13. What is the time value of this option?
A$13 — the entire option premium is time value
B$10 — the intrinsic value equals the stock price minus the strike
C$3 — intrinsic value is $10, so the remaining $3 is time value
D$23 — time value is the strike plus the option premium
Intrinsic value = max(S − K, 0) = max(60 − 50, 0) = $10. This is the immediate exercise payoff. The market price is $13, which exceeds intrinsic value by $3. That $3 is time value — the premium for the possibility that the stock climbs further before expiration. Option price = intrinsic value + time value is the fundamental decomposition.
Question 2 Multiple Choice
A company announces unexpectedly large earnings uncertainty ahead. The stock price remains unchanged, but implied volatility on its options doubles. What happens to the time value of its at-the-money call options?
ATime value decreases — higher volatility makes the option riskier and therefore less valuable to hold
BTime value increases — greater potential movement raises the value of the right (but not obligation) to buy
CTime value is unchanged — only the stock price affects option value, not volatility
DIt depends on whether the option is in-the-money or out-of-the-money
Higher volatility always increases time value for both calls and puts. The reason is the asymmetric payoff structure: as an option holder, you benefit from large favorable moves but your downside is capped at the premium paid. If the stock might move ±30% instead of ±10%, the upside scenario is much better while the downside is still capped. This asymmetry means option holders gain from volatility — which is why buying options is often described as 'buying volatility.'
Question 3 True / False
An out-of-the-money option has zero intrinsic value but can still have a positive market price.
TTrue
FFalse
Answer: True
Intrinsic value is the immediate exercise payoff. For an out-of-the-money option, exercising right now is worthless (max(S − K, 0) = 0 for a call when S < K). But the option still has time value — the possibility that the underlying price could move favorably before expiration. As long as time remains and any chance exists of expiring in-the-money, traders will pay a positive premium.
Question 4 True / False
As an option approaches its expiration date, its time value increases because uncertainty about the final outcome grows.
TTrue
FFalse
Answer: False
The opposite is true. Time value erodes as expiration approaches — this is theta decay. With less time remaining, there are fewer chances for the underlying to move favorably. Near expiration, an out-of-the-money option is nearly worthless because there is almost no time left for the stock to recover. Theta decay actually accelerates in the final days before expiration.
Question 5 Short Answer
Why does higher volatility in the underlying asset always increase the time value of an option, regardless of whether it is a call or a put?
Think about your answer, then reveal below.
Model answer: Because of the asymmetric payoff structure. An option holder benefits from large moves in the favorable direction but loses only the fixed premium if the move goes the wrong way. Higher volatility increases the probability of large favorable moves without increasing the maximum loss (still capped at the premium). This asymmetry means option holders always benefit from volatility — more potential upside, same capped downside.
For a call: higher volatility means the stock might rise much more, increasing the call's payoff; if it falls, you just don't exercise. For a put: higher volatility means the stock might fall much more, increasing the put's payoff; if it rises, you don't exercise. In both cases, the holder captures the favorable tail and ignores the unfavorable tail. This is why implied volatility is the central pricing variable in options markets.