Explanation

This question deals with the volatility smile phenomenon and how it differs between equity options and FX options.

Key Concepts:

1. Volatility Smile Patterns:

   • Equity options (like FBX stock): Typically exhibit a volatility skew where implied volatility is higher for out-of-the-money put options (lower strike prices) compared to out-of-the-money call options. This creates an asymmetric smile.
   • FX options (like EUR/JPY): Typically exhibit a symmetric volatility smile where implied volatility is higher for both deep out-of-the-money calls and puts compared to at-the-money options.

2. Deep Out-of-the-Money Call Options:

   • For equity options: The implied risk-neutral distribution has fatter left tails (higher probability of large downward moves) but thinner right tails (lower probability of large upward moves) compared to the lognormal distribution.
   • For FX options: The implied risk-neutral distribution has fatter tails on both sides (higher probability of both large upward and downward moves) compared to the lognormal distribution.

Analysis:

• FBX Stock Options: When using the lognormal distribution instead of the implied risk-neutral distribution for deep OTM calls, you're underestimating the probability of large upward moves (since the implied distribution has thinner right tails for equities). This means you'll price the option relatively low.

• EUR/JPY FX Options: When using the lognormal distribution instead of the implied risk-neutral distribution for deep OTM calls, you're underestimating the probability of large upward moves (since the implied distribution has fatter right tails for FX). This means you'll price the option relatively low.

Wait, let me reconsider this carefully.

Actually, the correct reasoning is:

• Equity options: The implied risk-neutral distribution has fatter left tails but thinner right tails than lognormal. For deep OTM calls, using lognormal would overestimate the probability of reaching the strike price, thus pricing the option relatively high.

• FX options: The implied risk-neutral distribution has fatter tails on both sides than lognormal. For deep OTM calls, using lognormal would underestimate the probability of reaching the strike price, thus pricing the option relatively low.

Therefore, the correct answer is A: Price the option on FBX relatively high and price the option on EUR/JPY relatively low.