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Arisk committee of the board of company ABC is discussing the difference between pricing deep out-of-the-money call options onABC stock and pricing deep out-of-the-money call options on the USD/GBP foreign exchange rate using the Black-Scholes-Merton (BSM) model. The committee considers pricing each of these 2 options based on two distinct probability distributions of underlying asset prices at the option expiration date: Alognormal 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, which of the following is correct?

A) The price of the option on ABC would relatively be high and the price of the option on USD/GBP would relatively be low comparing to those computed from the lognormal counterparts.》》》想?yún)⒓尤谲SFRM培訓(xùn)班點我咨詢

B) The price of the option on ABC would relatively be low and the price of the option on USD/GBD would relatively be high comparing to those computed from the lognormal counterparts.

C) The price of the option on ABC would relatively be low and the price of the option on USD/GBD would relatively be low comparing to those computed from the lognormal counterparts.

D) The price of the option on ABC would relatively be high and the price of the option on USD/GBD would relatively be high comparing to those computed from the lognormal counterparts.

掃碼參與

答案：B 【資料下載】FRM一級思維導(dǎo)圖PDF版

解析：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.

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