Answer-first summary for fast verification
Answer: The price of the option on ABC stock would be relatively high and the price of the option on USD/GBP FX rate would be relatively low compared to those computed from the lognormal counterparts.
## Explanation This question addresses the volatility smile phenomenon and how it differs between equity options and foreign exchange options. ### Key Concepts: 1. **Volatility Smile**: The pattern where implied volatility varies with strike price, creating a "smile" shape when plotted. 2. **Equity Options (ABC stock)**: - Typically exhibit a **volatility skew** rather than a symmetric smile - For deep out-of-the-money call options, the implied volatility is **lower** than at-the-money options - This reflects market concern about downside risk (put protection) more than upside potential 3. **Foreign Exchange Options (USD/GBP)**: - Typically exhibit a more **symmetric volatility smile** - For deep out-of-the-money call options, the implied volatility is **higher** than at-the-money options - This reflects equal concern about large movements in either direction ### Analysis: When using the implied risk-neutral distribution from the volatility smile instead of the lognormal distribution: - **For ABC stock options**: The implied distribution assigns **lower probabilities** to extreme upside moves compared to the lognormal distribution, leading to **lower option prices** for deep OTM calls. - **For USD/GBP FX options**: The implied distribution assigns **higher probabilities** to extreme moves in both directions compared to the lognormal distribution, leading to **higher option prices** for deep OTM calls. Therefore, the correct relationship is that the price of the option on ABC stock would be relatively **low** and the price of the option on USD/GBP FX rate would be relatively **high** compared to those computed from the lognormal counterparts. **Note**: The provided option A states the opposite relationship, which suggests there may be an error in the question or answer choices. Based on standard financial theory, the correct relationship should be: - Equity OTM calls: Lower price with implied distribution - FX OTM calls: Higher price with implied distribution
Author: LeetQuiz .
Ultimate access to all questions.
No comments yet.
A risk manager of company ABC is discussing the difference between pricing deep out-of-the-money call options on ABC stock and pricing deep out-of-the-money call options on the USD/GBP foreign exchange (FX) rate using the Black-Scholes-Merton model. The manager considers pricing each of these two options based on two distinct probability distributions of underlying asset prices at the option expiration date: a lognormal probability distribution, and an implied risk-neutral probability distribution obtained from the volatility smile for each aforementioned option of the same maturity and the same moneyness. If the implied risk-neutral probability distribution is used instead of the lognormal distribution, which of the following is correct?
A
The price of the option on ABC stock would be relatively high and the price of the option on USD/GBP FX rate would be relatively low compared to those computed from the lognormal counterparts.
B