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Answer: 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.
The correct answer is B. When pricing options, using an implied risk-neutral probability distribution instead of a lognormal distribution can lead to different pricing outcomes based on the characteristics of the underlying asset. For deep out-of-the-money call options on ABC stock, the implied distribution derived from the equity options' volatility smile has a heavier left tail and a less heavy right tail compared to a lognormal distribution. This results in a lower option price when using the implied distribution compared to the lognormal distribution. Conversely, for deep out-of-the-money call options on the USD/GBP foreign exchange rate, the implied distribution from the foreign currency options' volatility smile has heavier tails than a lognormal distribution. This leads to a higher option price when using the implied distribution compared to the lognormal distribution. This understanding is crucial for accurately pricing options and managing market risk, as it reflects the market's expectations and the skewness of potential price movements.
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The risk committee of company ABC's board is currently analyzing the variance in the pricing of deep out-of-the-money call options on both ABC's stock and the USD/GBP foreign exchange rate. They are utilizing the Black-Scholes-Merton model to facilitate this examination. The committee is considering the valuation of these options based on two different probability distributions for the asset prices at expiration: a lognormal distribution and an implied risk-neutral distribution derived from the volatility smile, with the same maturity and moneyness for each option. What will be the accurate outcome if the implied risk-neutral distribution is used instead of the lognormal distribution?
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
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.
C
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 low compared to those computed from the lognormal counterparts.
D
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 high compared to those computed from the lognormal counterparts.