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Financial Risk Manager Part 2

Financial Risk Manager Part 2

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  1. When the risk committee of Company ABC's board deliberates the valuation discrepancies between deep out-of-the-money call options for ABC shares and deep out-of-the-money call options for the USD/GBP currency pair, they employ the Black-Scholes-Merton model. Specifically, they consider using two distinct probability distributions for the underlying asset prices at the expiration of these options: a traditional lognormal distribution and a risk-neutral implied probability distribution, each derived from the volatility smile for the respective options, assuming the same maturity and moneyness. What would be the correct outcome if the risk-neutral implied probability distribution is used instead of the lognormal distribution?

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Explanation:

The correct answer is B. When pricing deep out-of-the-money call options, using the implied risk-neutral probability distribution derived from the volatility smile leads to different pricing outcomes compared to using a lognormal distribution. For equity options like those on ABC stock, the implied distribution has a heavier left tail and a less heavy right tail than a lognormal distribution. This results in a lower price for deep-out-of-the-money call options when using the implied distribution compared to the lognormal distribution. Conversely, for foreign currency options like those on the USD/GBP FX rate, the implied distribution has heavier tails than a lognormal distribution. This causes deep-out-of-the-money call options to be priced relatively higher 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 view of potential price movements and the associated risks.

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