Volatility Smile Flashcards
What is the BSM method of option pricing?
The BSM method calculates the value of an option based on certain assumptions, including constant volatility and a lognormal distribution of asset prices.
How can the BSM model be used to observe market option prices?
By observing option prices in the market, the BSM model can calculate the implied volatility needed to match observed prices.
What is implied volatility?
Implied volatility is the volatility calculated from the market price of an option using the BSM model. It reflects the market’s expectation of future volatility.
How does implied volatility generally behave?
Implied volatility typically varies in a non-linear fashion, and it’s often represented as a volatility smile or smirk.
What is a volatility smile?
A volatility smile is a graphical representation of implied volatility where strike price is plotted on the x-axis and implied volatility on the y-axis. Implied volatility is higher for options that are deeply in-the-money or out-of-the-money.
What does a volatility smile look like for European options?
It shows relatively low implied volatility for at-the-money options, with volatility increasing as the option becomes more in-the-money or out-of-the-money.
What is the implied volatility pattern for foreign currency options?
Deep out-of-the-money call options for foreign currencies tend to have higher implied volatilities because the probability of payoff is higher in the tails of the distribution, leading to higher option prices.
Why is implied volatility for foreign currency options different from a lognormal distribution?
Because exchange rates exhibit jumps and volatility is stochastic, unlike the assumptions of constant volatility and smooth asset price changes in a lognormal distribution.
What caused the volatility smile to emerge for equity options?
Prior to the 1987 stock market crash, there was no noticeable volatility smile. After the crash, the pattern became evident, showing higher implied volatility for options with lower strike prices.
What is the pattern of implied volatility for equity options?
Implied volatility decreases as the strike price increases. Options with lower strike prices have significantly higher implied volatility than those with higher strike prices.
What is leverage and how does it affect volatility in equity options?
Leverage refers to the amount of debt a company uses. As a company’s equity decreases in value, its leverage increases, making the equity more risky and its volatility higher. This explains the downward-sloping volatility smirk for equity options.
What is “crashophobia” and how does it affect equity options?
“Crashophobia” refers to the market’s fear of a crash, leading to increased demand for out-of-the-money put options. This higher demand pushes up the price of these options, contributing to the volatility smirk.
What is the volatility term structure?
The volatility term structure shows how implied volatility changes with the time to maturity of the option. It generally increases as maturity increases when short-dated volatilities are low, and decreases when short-dated volatilities are high.
How do volatility surfaces combine with volatility smiles?
Volatility surfaces combine the volatility smile with the term structure, showing the volatilities used in option pricing across different strike prices and maturities
