Investing: Option Pricing Factors

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Questions and Answers

What is the upper price bound for a call option?

It is based on the volatility of the stock.

It can never exceed the strike price.

It is determined by the risk-free interest rate.

It is capped at the current stock price. (correct)

For a European put option, what is the maximum value it can reach?

The strike price. (correct)

The risk-free interest rate compounded.

The current stock price.

The present value of the strike price today. (correct)

What influences the lower boundary of a non-dividend paying European call option?

The current stock price only.

The maximum of $0 and the difference of stock price and present value of the strike price. (correct)

The risk-free interest rate alone.

The time to expiration alone.

Which of the following factors does NOT affect the price of a stock option?

The historical price of the stock. Signup and view all the answers

What is the significance of the strike price in determining option prices?

It is the price at which an option can be exercised. Signup and view all the answers

In the context of an American put option, what is the maximum price it can hold?

The strike price. Signup and view all the answers

What is the risk-free interest rate's effect on option pricing?

It lowers the present value of strike prices causing call options to increase. Signup and view all the answers

What defines the lower boundary of a European put option on a non-dividend paying stock?

The maximum of $0 and the difference between strike price and adjusted stock price. Signup and view all the answers

What is the objective of put-call parity?

To ensure options with the same strike price and time to maturity have equivalent value Signup and view all the answers

Which formula correctly represents the lower bound for a European call option?

$max(S_0 - K e^{-rT}, 0)$ Signup and view all the answers

What is the implication when a European put option is overpriced compared to a European call option?

Arbitrage opportunities exist Signup and view all the answers

When is it optimal to exercise a put option early?

When the stock price decreases significantly Signup and view all the answers

In the context of American options, what prevents the early exercise of an American call option on a non-dividend paying stock?

The time value of money and insurance against price drops Signup and view all the answers

What condition generally makes the early exercise of a put option less beneficial?

When the stock price is increasing Signup and view all the answers

What is one primary reason an American call option on a dividend-paying stock might be exercised early?

To maximize the cash flow from dividends Signup and view all the answers

Which is NOT a characteristic of the lower bound of a European put option?

It is irrelevant to the strike price of the option. Signup and view all the answers

What does the formula $c + K e^{-rT} = p + S_0$ represent?

The relationship between the values of call and put options in arbitrage Signup and view all the answers

What is one reason why an American put option may be exercised early?

To protect against further stock price decline Signup and view all the answers

Study Notes

Factors Affecting Option Prices

Six factors influence stock option prices:
- Current stock price (S₀)
- Strike price (K)
- Time to expiration (T)
- Stock price volatility
- Risk-free interest rate (r)
- Expected dividends

Upper Price Bounds

Call Options: A call option's price (C) cannot exceed the stock price (S₀).
- C ≤ S₀; c ≤ So
- Otherwise, arbitrage opportunities exist.
Put Options (American): A put option's value (P) cannot exceed the strike price (K).
- P ≤ K
Put Options (European): A European put option's value cannot exceed the present value of the strike price (K).
- P ≤ Ke⁻^rT

Lower Bounds (Non-Dividend Paying Stocks)

Call Options: A call option's value (c) cannot be negative.
- c ≥ max(S₀ - K e⁻^rT, 0)
- The worst case is expiration with zero value.
Put Options (European):
- p ≥ max(K e⁻^rT - S₀, 0)
Example Calculations: Provided examples illustrate how to determine lower bounds using the formulas provided for various stock prices, strike prices, time to maturity, and risk-free interest rates.

Put-Call Parity

Relationship: A theory stating the relationship between the prices of a call and put option with the same strike price and time to maturity:
- c + Ke⁻^rT = p + S₀
Formula rearrangements are used to evaluate options:
- p = c + Ke⁻^rT - S₀
- c = p + S₀ - Ke⁻^rT
Arbitrage: Mispricing between these options indicates arbitrage opportunities for profit.

American Options on Dividend-Paying Stocks

Impact of Dividends: Dividends affect the option's lower bounds.
American Calls: Generally, American calls are never optimally exercised before expiration on non-dividend paying stocks, valuing them like European calls.
- Lower Bound: c ≥ max(S₀ - D - Ke⁻^rT, 0)
American Puts: American puts may be exercised early.
- Lower Bound: p ≥ max(K - S₀, 0)
- Early exercise is more attractive as S₀ decreases, r increases, and volatility decreases.
Optimal Exercise Conditions: When dividends are involved, it may be optimal to exercise early on American options.
- Specific conditions, including ex-dividend dates, may make early exercise optimal for American calls. This differs from some scenarios where this is not the case.

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Description

This quiz explores the factors affecting stock option prices and the upper and lower price bounds of call and put options. Test your understanding of concepts such as the current stock price, strike price, and their impact on option valuations. Ideal for students in finance or investing courses.