Questions and Answers
For an American call option, what is the minimum value when the option is out of the money?
What is the correct formula for determining the intrinsic value of an in-the-money call option?
When calculating the minimum value of a European put option that is out of the money, which of the following is true?
What defines the maximum value of a put option according to the given content?
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In the case of an arbitrage opportunity, what condition must be met regarding the contract price and the intrinsic value of the call option?
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What does it mean when a call option is described as 'out of the money'?
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What is the intrinsic value of a put option that is 'in the money'?
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Which of the following statements about time value is true?
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Which factor does NOT contribute to the changing intrinsic value of an option?
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Why is it essential to understand the concept of option moneyness?
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What component must be included in the value calculation for a European option that is commonly overlooked in exams?
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For a put option, how is the value determined at expiration?
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What happens to the cost of options as the time to expiration decreases?
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In the context of call options, what is the relationship between exercise price and option value?
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What is indicated by a higher premium for a put option?
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Study Notes
Stock Options Overview
- Risk-Free Rate: Assumed to be 5%, often sourced from ASX benchmark rates.
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Call Options: Grant the right to buy assets at a predetermined exercise price.
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Moneyness:
- At the Money: Stock price equals exercise price.
- In the Money: Stock price exceeds exercise price, allowing purchase at a lower cost.
- Out of the Money: Stock price is lower than exercise price, making option unexecuted.
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Moneyness:
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Put Options: Grant the right to sell assets at a predetermined exercise price.
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Moneyness:
- At the Money: Stock price equals exercise price.
- In the Money: Stock price is lower than exercise price, allowing selling at a higher price.
- Out of the Money: Stock price exceeds exercise price, making option unexecuted.
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Moneyness:
Intrinsic Value and Time Value
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Intrinsic Value: Value of the option if it were exercised today.
- Call Option: If in/out of the money, intrinsic value is the difference (Spot price - PV of Exercise Price).
- Put Option: If in/out of the money, intrinsic value is the difference (PV of Exercise Price - Spot price).
- Time Value: Reflects uncertainty about future stock prices, and tends to be higher with longer expiration periods.
Option Boundaries
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Minimum Value:
- Call Options:
- American: Maximum of 0 or (Spot Price - Exercise Price).
- European: Maximum of 0 or (Spot Price - PV of Exercise Price).
- Put Options:
- American: Maximum of 0 or (Exercise Price - Spot Price).
- European: Maximum of 0 or (PV of Exercise Price - Spot Price).
- Call Options:
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Maximum Value:
- Call Option: Absolute maximum equals Spot Price.
- Put Option: Absolute maximum equals Exercise Price.
Factors Affecting Option Value
- Time to Expiration: Longer time generally increases option value due to greater uncertainty.
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Exercise Price:
- Call Options: Lower exercise price raises option value.
- Put Options: Higher exercise price raises option value.
- Premiums: The premium of an option typically correlates inversely with exercise price.
Dividends and Early Exercise
- Dividends: Impact option value by changing the intrinsic value based on whether an option is executed before or after a dividend payout.
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Early Exercise:
- American Options can be exercised before expiration, providing potential advantages, particularly with dividends.
- Early exercise for American Puts is influenced by dividend expectations.
Interest Rates
- Call Options: Higher interest rates enhance call option values as they allow for the allocation of capital towards interest-earning investments while waiting for the right moment to buy the asset.
- Put Options: Higher interest rates reduce put option values since selling now could allow investment in higher yield opportunities instead of waiting.
Stock Volatility
- Call Options: Increased volatility enhances value due to the potential for higher profits when stock prices rise.
- Put Options: Increased volatility also enhances value by limiting losses to the premium paid while allowing for profit if prices decline.
Put-Call Parity
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A critical concept used to determine the price relationship between call and put options.
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Portfolio A: Consists of European Put and holding a share.
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Portfolio B: Consists of European Call and a bond earning the risk-free rate, establishing a pricing relationship between these options.### Portfolio Payoffs
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Portfolio A (Put):
- In-the-money condition (ST < X): Payout is equal to the exercise price (X).
- Out-of-the-money condition (ST > X): Payout is equal to the stock price (ST).
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Portfolio B (Call):
- Out-of-the-money condition (ST < X): Payout equals the exercise price (X), as purchasing is not favorable.
- In-the-money condition (ST > X): Payout equals the stock price (ST).
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Payoff comparison shows both portfolios provide the same outcomes:
- For ST < X: Payout is X.
- For ST > X: Payout is ST.
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The relationship between portfolios can be expressed as:
- PV Stock + Put Option = Call Option + PV Bond.
European Options Valuation
- European Put Value: Call Option + Bond Value - Stock Price.
- European Call Value: Stock Price + Put Option Value - Bond Value.
American Options Consideration
- American options can factor in the present value of dividends.
Example 1: ANZ Call and Put
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ANZ Call:
- Call cost is $0.52.
- Current spot price is $15.74.
- Time to expiration is approximately 86 days (86/365).
- Exercise price is $16.0.
- Risk-free rate assumed at 5%.
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ANZ Put:
- Put cost is $0.6.
- Current spot price is $15.74.
- Time to expiration matches the call option.
- Exercise price is $16.0.
- Risk-free rate assumed at 5%.
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Cost comparison: Put is more expensive due to being in-the-money, while call is out-of-the-money.
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Let's verify if Put-Call Parity holds:
- Call option + Bond value: $0.52 + $16 = $16.52.
- Put option + Share value: $0.6 + $15.74 = $16.34.
- Call + Present Value of Bond: $0.52 + PV(Bond) = $15.82; equals $16.34.
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Conclusion: Put-Call Parity holds in this scenario; they align, indicating no arbitrage opportunities exist.
Example 2: At the Money Options
- To compare an at-the-money call option and put option:
- Rearrange the relevant formula.
- When at-the-money, spot price (S) equals exercise price (X).
- Thus, the Call Price is equal to the Put Price plus the risk-free rate.
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Description
This quiz covers fundamental concepts of stock options, including definitions of call and put options, and the terminology of 'at the money', 'in the money', and 'out of the money'. It also discusses the role of the risk-free rate and how to find it through the ASX website. Test your knowledge on these essential investment concepts.
