Answer-first summary for fast verification
Answer: The implied distribution has a heavier left tail and a heavier right tail.
## Explanation This question describes a **volatility smile** pattern where implied volatility is higher for both deep in-the-money and deep out-of-the-money options compared to at-the-money options. This pattern is characteristic of **leptokurtic distributions** (fat-tailed distributions). ### Key Points: 1. **Volatility Smile Pattern**: When implied volatility increases for both ITM and OTM options, it indicates that the market expects more extreme price movements than what a lognormal distribution would predict. 2. **Distribution Characteristics**: - A lognormal distribution has relatively thin tails - The observed volatility smile suggests the actual distribution has **fatter tails** (both left and right) - This means both extreme downside (left tail) and extreme upside (right tail) movements are more likely than predicted by the lognormal distribution 3. **Black-Scholes-Merton Assumption**: The BSM model assumes lognormal distribution of asset prices, but the observed volatility smile indicates this assumption is violated. 4. **Correct Answer Analysis**: - **Heavier left tail** = higher probability of extreme downside moves - **Heavier right tail** = higher probability of extreme upside moves - This matches the volatility smile pattern where both deep ITM and deep OTM options have higher implied volatilities Therefore, the implied distribution has **both heavier left and right tails** compared to a lognormal distribution with the same mean and standard deviation.
Author: LeetQuiz .
Ultimate access to all questions.
No comments yet.
A risk analyst at an investment bank is examining the assumptions the bank uses in its foreign exchange (FX) option pricing model. Currently, the implied volatility in a particular FX pair is relatively low if an option is at-the-money and becomes progressively higher as the option moves either more in-the-money or more out-of-the-money. How does the distribution of option prices on this FX pair implied by the Black-Scholes-Merton model compare to a lognormal distribution with the same mean and standard deviation?
A
The implied distribution has a heavier left tail and a less heavy right tail.
B
The implied distribution has a heavier left tail and a heavier right tail.
C
The implied distribution has a less heavy left tail and a heavier right tail.
D
The implied distribution has a less heavy left tail and a less heavy right tail.