Financial Risk Manager Part 2

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Explanation:

Explanation

This question addresses the volatility smile phenomenon and how it differs between equity options and foreign exchange options.

Key Concepts:

Volatility Smile: The pattern where implied volatility varies with strike price, creating a "smile" shape when plotted.
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
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

Explanation:

Explanation

This question addresses the volatility smile phenomenon and how it differs between equity options and foreign exchange options.

Key Concepts:

Volatility Smile: The pattern where implied volatility varies with strike price, creating a "smile" shape when plotted.
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
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.

Equity OTM calls: Lower price with implied distribution
FX OTM calls: Higher price with implied distribution

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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?

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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.

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