Questions and Answers
What is the intrinsic value of a European Call option when the spot price is equal to the exercise price?
When is a European Put option considered to be in the money?
Which of the following factors does NOT contribute to the time value of an option?
What happens to the intrinsic value of an out of the money European Call option?
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How is the total price (premium) of an option calculated?
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Which statement is true regarding American vs. European options?
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What is the absolute minimum value of any option?
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What determines the minimum value of a European call option at expiration?
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Which statement accurately describes the maximum value of an American put option at expiration?
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How does the time to expiration affect the value of options?
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What is the relationship between the exercise price and the premium of a call option?
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In what situation is a call option classified as 'in the money'?
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What characterizes the maximum value for a European put option at expiration?
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Which of the following statements correctly compares the minimum value of American and European put options?
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What indicates that you should sell a put option at a higher exercise price?
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What impact does a lower exercise price have on the premium of a call option?
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How does a put option with a higher exercise price generally behave in terms of premium?
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What effect does early exercise of an American option have when a dividend is approaching?
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In the context of interest rates, how does the value of a put option change?
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What is the primary benefit of purchasing a call option instead of the underlying asset directly?
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Why is the volatility of the market a significant factor in determining option premiums?
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How does the presence of dividends affect the value of call options?
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What differentiates American options from European options when considering their exercise features?
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What is the relationship between the exercise price and the price of a put option?
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Study Notes
Options Types
- European Call (Ce) and Put (Pe) do not allow early exercise before expiration.
- American Call (Ca) and Put (Pa) allow early exercise at any time before expiration.
Intrinsic Value of Options
-
European Call (Ce):
- In the money (St > X): Intrinsic Value = St - PV(X)
- At/near the money (St ~ X or St = X): Intrinsic Value = max(St - PV(X), 0)
- Out of the money (St < X): Intrinsic Value = 0
-
European Put (Pe):
- In the money (St < X): Intrinsic Value = PV(X) - St
- At/near the money (St ~ X or St = X): Intrinsic Value = max(PV(X) - St, 0)
- Out of the money (St > X): Intrinsic Value = 0
Time Value of Options
- Represents potential for increase in value before expiration due to volatility, time, and interest rates.
- Total option premium is comprised of Intrinsic Value + Time Value.
- Time value is maximized for options that are at the money and decreases closer to expiration.
Option Boundaries
-
Minimum value of any option is 0.
-
Call Option:
- American Option: Minimum = max(0, St - X)
- European Option: Minimum = max(0, St - PV(X))
-
Put Option:
- American Option: Minimum = max(0, X - St)
- European Option: Minimum = max(0, PV(X) - St)
Maximum Values of Options
-
Call Option:
- Maximum = Stock Price (So).
- Maximum at expiration = max(0, So - X).
-
Put Option:
- Maximum = Exercise Price (X).
- Maximum at expiration = max(0, X - St).
Time to Expiration
- Longer time to expiration typically leads to higher option values due to increased uncertainty.
- Shorter time causes options to be cheaper due to decrease in time value.
Exercise Price Effect on Option Value
- Call Options: Lower exercise prices result in higher values.
- Put Options: Higher exercise prices result in higher values.
Premiums of Options
- Premiums depend on exercise price, spot price, volatility, time to expiration, and interest rates.
- For calls, higher exercise prices lead to lower premiums, and lower exercise prices lead to higher premiums.
- For puts, higher exercise prices lead to higher premiums, and lower exercise prices lead to lower premiums.
Impact of Dividends on Options
- Dividends affect the intrinsic value, with potential adjustments made to account for dividends paid before expiration.
- Call option value decreases with dividends as the underlying stock may fall in value after the dividend payment.
Early Exercise
- American options can be exercised early, which adds value compared to European options that cannot be exercised before expiration.
- Early exercise may be beneficial for American calls before dividend dates to capture dividends.
Interest Rates
- Higher interest rates generally lower put option values as immediate selling becomes more attractive.
- Calls can be advantageous as they allow investing freed-up funds elsewhere.
Volatility
- Higher volatility increases the value of both call and put options due to potential for larger price swings.
- Historical volatility reflects past movements while implied volatility reflects market expectations.
The Greeks
- Greeks measure sensitivity of option values to various factors:
- Delta: Sensitivity to spot price changes; ranges from 0 to 1.
- Gamma: Sensitivity of delta to stock price changes; highest at the money.
- Vega: Sensitivity to changes in volatility; highest value when an option is at the money.
- Rho: Sensitivity to changes in interest rates.
- Theta: Daily decrease in option value as expiration approaches.
Option Strategies
- Long Put: Right to sell; hopes for So < X.
- Short Call: Obligation to sell; hopes for So < X.
- Long Call: Right to buy; hopes for So > X.
- Short Put: Obligation to buy; hopes for So > X.
- Straddle: Buying a call and a put with the same strike price.
- Protective Put: Buying stock and a put to hedge.
- Covered Call: Selling a call while owning the stock to generate higher income.
- Strap: Buying two calls and one put for bullish sentiment.
- Strip: Buying two puts and one call for bearish sentiment.
Key Examples
- Call Option Example: An ANZ call with a lower exercise price ($15.50) may cost more than a higher one ($16.00) due to increased likelihood of profitability.
- Put Option Example: Similar principles apply where higher exercise prices will have more value for puts.
General Strategy Insights
- Profits can be made by identifying underpriced or overpriced options relative to their market value or through specific trading strategies.
These notes summarize the key concepts of options trading including valuation techniques, market behavior, and strategic approaches.
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Description
Test your understanding of options pricing with a focus on European call and put options. This quiz covers the intrinsic value calculations based on current market conditions and option types. Questions will explore scenarios such as in the money, at the money, near the money, and out of the money.
