Questions and Answers
What is the intrinsic value of a European Call option when the spot price (St) is less than the exercise price (X)?
Which factor does not directly influence the time value of an option?
What is the primary difference between the intrinsic value of European and American Put options when both are at the money?
When the total option premium is calculated, what portion is deducted to find the time value?
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Which statement about option boundaries is accurate?
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What determines the minimum value of an American call option when it is out of the money?
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At expiration, the maximum value of a European put option is equivalent to which value?
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Which statement about the effect of time to expiration on option value is correct?
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What is the relationship between exercise price and the value of an American put option?
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What is the maximum value of a call option at expiration?
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If two options have different exercise prices but the same stock and maturity, what is true about their values?
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What factor typically decreases the premium of a call option?
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What is the absolute minimum value of a put option when it is out of the money?
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What is the effect of time value on near expiration options?
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Study Notes
European and American Options
- European Call (Ce) and Put (Pe) options can only be exercised at expiration; American Call (Ca) and Put (Pa) options can be exercised anytime before expiration.
European Call Option (Ce)
-
Intrinsic Value:
- In the Money (St > X): Intrinsic Value = St - PV(X)
- At/near the Money (St ≈ X): Intrinsic Value = St - PV(X) or 0
- Out of the Money (St < X): Intrinsic Value = 0
- Out of the money calls provide no benefit as they are not exercised.
European Put Option (Pe)
-
Intrinsic Value:
- In the Money (St < X): Intrinsic Value = PV(X) - St
- At/near the Money (St ≈ X): Intrinsic Value = PV(X) - St or 0
- Out of the Money (St > X): Intrinsic Value = 0
- Negative intrinsic value is not possible.
Time Value of Options
- Represents potential for price increase before expiration due to volatility, remaining time, and interest rates.
- Formula: Option Premium = Intrinsic Value + Time Value
- Time value peaks when options are at the money and diminishes as expiration approaches.
Option Boundaries
- Minimum value for both options is 0.
- American Call Minimum: Max{0, (Spot price - Exercise Price)}
- European Call Minimum: Max{0, (Spot Price - PV(X))}
- Maximum for Call Options: Stock Price (So) at infinite maturity.
Value at Expiration
- Call Option Value: Max{0, (Spot Price - Exercise Price)} for both European and American.
- Put Option Value:
- European: Max{PV(X) - Spot Price}
- American: Max{Exercise Price - Spot Price}
Time to Expiration
- Longer time to expiration increases option value due to higher uncertainty and time value.
- Value decreases as expiration nears, particularly for options that are deep in or out of the money.
Effect of Exercise Price
- For Call Options, lower exercise prices result in higher option values due to increased "in the money" potential.
- For Put Options, higher exercise prices yield higher premiums, as selling at a higher price is more advantageous.
Option Premiums
- Call Options:
- Higher exercise price typically leads to a lower premium.
- Lower exercise price generally warrants a higher premium.
- Put Options:
- Higher exercise price leads to a higher premium, indicating higher "in the money" probability.
Impact of Dividends
- Dividends affect the value of options as they change the intrinsic value.
- Call options generally decrease in value prior to dividend payouts since intrinsic value considers dividends.
Early Exercise Considerations
- American options can be exercised early for potentially increased benefits, especially near dividend dates.
- American puts are beneficial to exercise early under certain market conditions, especially when stock prices are low.
Interest Rates
- Call options leverage capital, allowing investors to utilize funds productively while holding options.
- Higher interest rates reduce put option values due to lost opportunities from delayed sales.
Volatility
- Increased volatility raises the value of both call and put options as it enhances profit potential and limits losses to the premium paid.
These notes outline critical components of options trading and essential calculations for option pricing and evaluation.
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Description
Dive into the concepts of European and American options. This quiz covers intrinsic value calculations for both call and put options, discussing various scenarios of 'in the money', 'at the money', and 'out of the money'. Test your understanding of how these terms apply to option pricing!
