
Explanation:
B is correct. The implied distribution of the underlying equity prices derived using the general volatility smile of equity options has a heavier left tail and a less heavy right tail than a lognormal distribution of underlying prices. Therefore, using the implied distribution of prices causes deep-out-of-the-money call options on the underlying to be priced relatively low compared with using the lognormal distribution. The implied distribution of underlying foreign currency prices derived using the general volatility smile of foreign currency options has heavier tails than a lognormal distribution of underlying prices. Therefore, using the implied distribution of prices causes deep-out-of-the-money call options on the underlying to be priced relatively high compared with using the lognormal distribution.
Learning Objective: Describe characteristics of foreign exchange rate distributions and their implications on option prices and implied volatility.
Reference: John Hull, Options, Futures, and Other Derivatives, 11th Edition (New York: Pearson, 2022). Chapter 20 - Volatility Smiles
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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.