Lecture 5

Question 1

What are the Option Greeks?

Answer 1

The Greeks are sensitivity measures for option prices, derived from the Black-Scholes model, indicating how an option’s value responds to changes in various factors.

Question 2

What does Delta (∆) measure?

Answer 2

Delta measures the rate of change of the option price with respect to the underlying asset’s price.

Question 3

What does Gamma (Γ) measure?

Answer 3

Gamma measures the rate of change of Delta as the stock price changes.

Question 4

What does Vega (ν) measure?

Answer 4

Vega measures the sensitivity of the option price to changes in the underlying asset’s volatility.

Question 5

What does Theta (Θ) measure?

Answer 5

Theta measures the rate of change of the option price with respect to time, often called “time decay”.

Question 6

What does Rho (ρ) measure?

Answer 6

Rho measures the sensitivity of the option price to changes in the risk-free interest rate.

Question 7

What is a Delta-neutral portfolio?

Answer 7

A portfolio where the total Delta is zero, making it insensitive to small changes in the underlying asset’s price.

Question 8

How is a Delta-neutral position achieved?

Answer 8

By balancing the Deltas of all positions in the portfolio so the total Delta equals zero.

Question 9

What happens to a Delta-neutral portfolio when the stock price changes?

Answer 9

The portfolio remains unaffected by small changes in the stock price.

Question 10

What is the role of Delta in hedging?

Answer 10

Delta helps create a hedge that offsets price changes in the underlying asset by balancing the portfolio’s exposure.

Question 11

What does high Gamma indicate?

Answer 11

High Gamma means the Delta of an option changes quickly, requiring more frequent adjustments to maintain neutrality.

Question 12

How does Gamma influence a portfolio?

Answer 12

Gamma affects how much Delta will change with stock price movements, impacting how often the portfolio needs to be rebalanced.

Question 13

What is the effect of high Gamma on hedging strategies?

Answer 13

High Gamma requires more frequent rebalancing to maintain Delta-neutral positions.

Question 14

How can you neutralize Gamma in portfolio?

Answer 14

By adding positions with offsetting Gamma values, such as buying or selling other options.

Question 15

What is the role of Vega in options pricing?

Answer 15

Vega shows how much the price of an option changes in response to changes in the volatility of the underlying asset.

Question 16

What happens to an option price when Vega increases?

Answer 16

The price of the option increases as volatility rises.

Question 17

How does volatility impact options pricing?

Answer 17

Higher volatility increases the value of options due to the increases potential for larger price movements in the underlying asset.

Question 18

What does Theta measure in options trading?

Answer 18

Theta measures the time decay of an option, showing how much the option’s price decreases as expiration approaches.

Question 19

How does Theta affect long options positions?

Answer 19

Theta causes the value of long options to decrease as expiration nears.

Question 20

How does Theta impact short options positions?

Answer 20

Theta benefits short options positions because the option loses value over time, which helps the short seller.

Question 21

What does Rho measure in options pricing?

Answer 21

Rho measures the sensitivity of the option price to changes in the risk-free interest rate.

Question 22

How does a rise in interest rates affect call options?

Answer 22

A rise in interest rates increases the price of call options.

Question 23

How does a rise in interest rates affect put options?

Answer 23

A rise in interest rates decreases the price of put options.

Question 24

What is Delta-Gamma hedging?

Answer 24

A strategy that neutralizes both Delta and Gamma to reduce risk from small and large stock price movements.

Question 25

How does Delta-Gamma hedging help manage risk?

Answer 25

By neutralizing both Delta and Gamma, this strategy reduces the risk of both small and large price changes.

Question 26

What is the trade-off using Delta-Gamma neutral strategies?

Answer 26

Requires more frequent adjustments and incurs higher transaction costs.

Question 27

Why is Delta-neutral hedging not enough on its own?

Answer 27

It does not account for changes in Gamma, Vega, or Theta, which can still expose the portfolio to risks.

Question 28

What is a dynamic hedge?

Answer 28

A dynamic hedge involves continuously adjusting the portfolio to account for changes in the stock price, volatility, or time to expiration.

Question 29

What is the effect of increasing volatility on options?

Answer 29

Increasing volatility raises the value of options, particularly for those with longer expirations.

Question 30

How does time decay affect long and short options differently?

Answer 30

Time decay reduces the value of long options but benefits short options positions as the options lose value over time.