Lecture 2

Question 1

What is a European call option?

Answer 1

A contract allowing the owner to buy an underlying asset at a prespecified price on a specific date.

Question 2

What is a European put option?

Answer 2

A contract allowing the owner to sell an underlying asset at a prespecified price on a specific date.

Question 3

How does an American option differ from a European option?

Answer 3

It can be exercised at any time before the expiration date.

Question 4

What does “in-the-money” mean for a call option?

Answer 4

The strike price is less than the underlying asset’s price, making exercise profitable.

Question 5

Define “in-the-money” for a put option.

Answer 5

The strike price is higher than the asset’s price, making it profitable to exercise.

Question 6

What is the payoff formula for a European call at expiration?

Answer 6

max(0, St - K), where St is the asset price at expiration and K is the strike price.

Question 7

What is intrinsic value in options?

Answer 7

The payoff if the option could be exercised immediately; it cannot be negative.

Question 8

What is time value in options?

Answer 8

The part of the option’s price above its intrinsic value, reflecting the potential for further profit before expiration.

Question 9

What is the no-arbitrage lower bound for a European call option?

Answer 9

max(0, S0 - K*e^-rT), where S0 is the spot price, K is the strike price and r is the risk-free rate.

Question 10

What is the upper bound of a call option price?

Answer 10

It cannot exceed the underlying asset’s current price S.

Question 11

How does the presence of dividends affect the lower bound of a call option?

Answer 11

The lower bound decreases by the present value of dividends.

Question 12

State put-call parity for European options.

Answer 12

c + K*e^-rT = p + S, where c and p are call and put prices, respectively.

Question 13

How does put-call parity help in constructing synthetic options?

Answer 13

By rearranging the formula, we can replicate a call or put option using a combination of positions.

Question 14

What is a covered call strategy?

Answer 14

Buy the stock while selling (short) a call option, providing income but capping upside potential.

Question 15

Describe a protective put strategy.

Answer 15

Buy the stock and buy a put option to protect against downside risk.

Question 16

What is a bull spread?

Answer 16

A strategy involving buying and selling calls (or puts) with different strikes to profit from moderate price rises.

Question 17

Explain a bear spread.

Answer 17

Involves buying and selling calls (or puts) with different strikes to profit from moderate price declines.

Question 18

What is a butterfly spread?

Answer 18

A position with three options at different strikes, profitable in low-volatility environments.

Question 19

Define a long straddle strategy.

Answer 19

Buying a call and put with the same strike, benefiting from large price movements in either direction.

Question 20

How does a strangle differ from a straddle?

Answer 20

It uses a call and put with different strikes, often cheaper but requires larger price movements to profit.

Question 21

What is convexity in options?

Answer 21

The idea that, for strikes K1 < K2 < K3, a weighted average of lower and higher strikes bounds the middle strike’s value.

Question 22

What is the upper bound for a put option price?

Answer 22

It is capped at the present value of the strike price (K*e^-rT)

Question 23

Why is early exercise for American call options on non-dividend stocks often suboptimal?

Answer 23

Exercising forfeits the time value of the option.

Question 24

What is the strike price condition for call options?

Answer 24

If K1 < K2, then the call price for K1 is greater than for K2 (higher strike price reduce option value)

Question 25

Describe a box spread strategy.

Answer 25

A combination of bull and bear spreads that results in a risk-free payoff, essentially replicating a loan.

Question 26

What is the purpose of a vertical spread?

Answer 26

To profit from directional price movements with a limited risk and profit potential.

Question 27

Define a calendar spread.

Answer 27

A strategy that involves options of the same strike but different maturities, benefiting from time decay differences.

Question 28

What is an ATM option?

Answer 28

An option where the strike price is equal to the current price of the underlying asset.

Question 29

Why might an investor choose a strangle over a straddle?

Answer 29

Strangles are cheaper due to the wider range for profit, though they require larger price movements to be profitable.

Question 30

What is a diagonal spread?

Answer 30

A strategy involving options with both different strikes and expirations, combining characteristics of vertical and calendar spreads.