The following two statements relate to financial derivatives. Choose the correct code for the statements being correct or incorrect. Statement I: When an option is allowed to be exercised only on the maturity date, it is called an American option. Statement II : If the option holder does not lose or gain whether he exercises his option or buys or sells the asset from the market, the option is said to be at-the-money.
Understanding Financial Derivatives: Options
This question asks us to evaluate two statements concerning financial derivatives, specifically focusing on options – their exercise style and their 'moneyness'. Let's analyze each statement carefully.
Analysis of Statement I: American Option Definition
Statement I says: "When an option is allowed to be exercised only on the maturity date, it is called an American option."
In the world of financial options, there are primarily two exercise styles:
- American Option: This type of option gives the holder the right to exercise the option at any time from the date of purchase up to and including the expiration date.
- European Option: This type of option gives the holder the right to exercise the option only on the expiration date.
Comparing the definition in Statement I with the standard definitions, we see that the description "exercised only on the maturity date" corresponds to a European option, not an American option.
Therefore, Statement I is incorrect.
Analysis of Statement II: At-the-Money Option Definition
Statement II says: "If the option holder does not lose or gain whether he exercises his option or buys or sells the asset from the market, the option is said to be at-the-money."
The 'moneyness' of an option describes its relationship between the underlying asset's current price (Spot Price, S) and the option's exercise price (Strike Price, K). The three main categories are:
- In-the-Money (ITM): Exercising the option would result in a positive intrinsic value. For a call option, S > K. For a put option, K > S.
- At-the-Money (ATM): The spot price of the underlying asset is equal to the strike price of the option, i.e., $\text{S} = \text{K}$. The intrinsic value is zero.
- Out-of-the-Money (OTM): Exercising the option would result in a zero intrinsic value (or a negative value if that were possible, but the option wouldn't be exercised). For a call option, S < K. For a put option, K < S.
Statement II describes a situation where exercising the option yields the same result as dealing with the asset in the market. Let's consider an at-the-money situation where $\text{S} = \text{K}$.
- For a Call Option: If $\text{S} = \text{K}$, exercising the call allows you to buy the asset for $\text{K}$. The market price is $\text{S}$, which is equal to $\text{K}$. So, you acquire the asset for $\text{K}$, and its market value is $\text{K}$. You don't gain or lose immediately compared to the market price of the asset itself.
- For a Put Option: If $\text{S} = \text{K}$, exercising the put allows you to sell the asset for $\text{K}$. The market price is $\text{S}$, which is equal to $\text{K}$. So, you sell the asset for $\text{K}$, and its market value is $\text{K}$. You don't gain or lose immediately compared to the market price of the asset itself.
In both at-the-money cases ($\text{S} = \text{K}$), the immediate outcome of exercising the option is neutral compared to the market price of the underlying asset. The intrinsic value of the option is zero. This aligns with the description in Statement II, where the holder "does not lose or gain whether he exercises his option or buys or sells the asset from the market".
Therefore, Statement II is correct.
Conclusion
Based on our analysis:
- Statement I, defining an American option, is incorrect.
- Statement II, defining an at-the-money option, is correct.
This aligns with the option that states Statement II is correct, but I is incorrect.
| Statement | Subject | Description Given | Correct Definition | Correctness |
|---|---|---|---|---|
| I | American Option | Exercised only on maturity date | Exercised any time up to maturity | Incorrect |
| II | At-the-Money Option | No gain/loss whether exercising or buying/selling from market | Spot Price = Strike Price ($\text{S} = \text{K}$) | Correct |
Revision Table: Key Option Concepts
| Concept | Definition | Condition (Call) | Condition (Put) |
|---|---|---|---|
| American Option | Exercisable any time up to expiry | - | - |
| European Option | Exercisable only on expiry | - | - |
| In-the-Money (ITM) | Positive intrinsic value if exercised | $\text{S} > \text{K}$ | $\text{K} > \text{S}$ |
| At-the-Money (ATM) | Zero intrinsic value if exercised | $\text{S} = \text{K}$ | $\text{S} = \text{K}$ |
| Out-of-the-Money (OTM) | Zero intrinsic value if exercised | $\text{S} < \text{K}$ | $\text{K} < \text{S}$ |
Additional Information: Intrinsic and Time Value
The price of an option is generally composed of two parts: Intrinsic Value and Time Value.
- Intrinsic Value: This is the immediate value obtained if the option were exercised right now. For a call, it is $\text{max}(\text{S} - \text{K}, 0)$. For a put, it is $\text{max}(\text{K} - \text{S}, 0)$. An option that is ITM has positive intrinsic value. An option that is ATM or OTM has zero intrinsic value.
- Time Value: This is the portion of the option's price that exceeds its intrinsic value. It represents the potential for the option to become more valuable before expiry. Time value decreases as the option approaches its expiry date.
An at-the-money option ($\text{S} = \text{K}$) has zero intrinsic value but can still have significant time value, especially if there is a lot of time remaining until expiry and the underlying asset's price is volatile.
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Choose the correct code for the following statements being correct or incorrect.
Statement I : FX Spot is an agreement between two parties to buy one currency against selling another currency at an agreed price for settlement on the spot date.
Statement II : The date of maturity of a forward contract is more than two business days in future.
