Lecture 6

Question 1

What is implied volatility in the context of the Black-Scholes (BS) model?

Answer 1

It is the volatility value that, when input into the BS formula, makes the calculated option price equal to the observed market price.

Question 2

How is implied volatility different from historical volatility?

Answer 2

Implied volatility reflects the market’s expectations for future price fluctuations, while historical volatility measures past price movements.

Question 3

What does implied volatility allow traders to compare across different options?

Answer 3

It allows traders to compare how expensive options are in a standardized way.

Question 4

What is the main input to the BS model that is “backed out” using implied volatility?

Answer 4

Volatility (Sigma)

Question 5

Does using implied volatility require the BS model to be accurate?

Answer 5

No, the BS model is just a “translator” for pricing: implied volatility is a derived value.

Question 6

What shape does the plot of implied volatility against strike price often resemble?

Answer 6

A smile, where implied volatility is higher for OTM or ITM options and lower for ATM options.

Question 7

Why does the volatility smile exist in the market?

Answer 7

Because the BS model’s assumption of constant volatility and log-normal price distribution doesn’t match real-world price dynamics (large swings and deep ITM/OTM)

Question 8

How does the volatility smile differ for equity options compared to currency options?

Answer 8

For equities, the smile is often asymmetric with higher IV for OTM puts. For currencies, the smile tends to be more symmetric.

Question 9

What does a steeper volatility smile imply about market sentiment?

Answer 9

Increased concern for extreme price movements, such as market crashes.

Question 10

Why do OTM put options generally have higher implied volatility than ATM options?

Answer 10

Because they are often used as protection against sharp price drops, increasing their demand and price.

Question 11

What is the volatility term structure?

Answer 11

The change in implied volatility depending on the option’s time to maturity.

Question 12

How does the volatility term structure behave in high-volatility periods and why?

Answer 12

It is typically downward-sloping, with IV decreasing as maturity increases. This could be because immediate uncertainty increases demand for near-term options.

Question 13

What is the volatility surface?

Answer 13

A 3D representation of implied volatility plotted against both strike price and time to maturity.

Question 14

What practical insights can traders gain from a volatility surface?

Answer 14

A more detailed understanding of pricing anomalies and market expectations across various strikes and maturities.

Question 15

How can the volatility surface change during periods of market stress?

Answer 15

The surface can steepen, showing much higher implied volatility for OTM options.

Question 16

What is the risk-neutral distribution in the context of option pricing?

Answer 16

A probability distribution of future prices where all investors are assumed to be indifferent to risk.

Question 17

How is the risk-neutral distribution derived from option prices?

Answer 17

By calculating the second derivative of option prices with respect to strike prices.

Question 18

What does the left tail of the risk-neutral distribution for equity options indicate?

Answer 18

A higher probability of sharp price drops compared to a log-normal distribution.

Question 19

What role does the butterfly spread play in calculating the risk-neutral distribution?

Answer 19

It helps approximate the second derivative of option prices.

Question 20

Why is the risk-neutral distribution “fatter” than the BS model’s assumed log-normal distribution?

Answer 20

Because markets price in higher probabilities of extreme events.

Question 21

What does the volatility smile reveal about the assumptions of the BS model?

Answer 21

That the model’s assumptions of constant volatility and log-normal price changes are incorrect.

Question 22

What is stochastic volatility?

Answer 22

A model extension where volatility itself follows a random process and is not constant over time.

Question 23

How does stochastic volatility explain the volatility smile?

Answer 23

It accounts for changing market conditions, like higher volatility during economic downturns.

Question 24

What are jump-diffusion models in option pricing?

Answer 24

Models that include sudden, large price changes in addition to regular price fluctuations.

Question 25

How do jump-diffusion models contribute to explaining volatility smiles?

Answer 25

They reflect market expectations for rare but significant price movements, like crashes.

Question 26

What does the CBOE VIX index measure?

Answer 26

The implied volatility of 30-day options on the S&P500, often called the “fear index”.

Question 27

How does combining stochastic volatility and jump-diffusion models improve market analysis?

Answer 27

By capturing both gradual changes in market conditions and sudden extreme events.

Question 28

Why might the implied volatility for OTM calls be high in commodity markets?

Answer 28

Due to concerns about sharp price increases caused by supply shocks.

Question 29

How do traders use implied volatility for risk management?

Answer 29

They monitor IV to anticipate market stress and hedge against extreme price movements.

Question 30

Why is the BS model still widely used despite its limitations?

Answer 30

It provides a simple framework and starting point for understanding and pricing options, with adjustments made through implied volatility and advanced models.