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Answer: Price the option on FBX relatively high and price the option on EUR/JPY relatively low.
## 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.
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A committee of risk management practitioners discusses the difference between pricing deep out-of-the-money call options on FBX stock and pricing deep out-of-the-money call options on the EUR/JPY foreign exchange rate using the Black-Scholes-Merton (BSM) model. The practitioners price these options based on two distinct probability distributions of underlying asset prices at the option expiration date:
Using the lognormal instead of the implied risk-neutral probability distribution will tend to:
A
Price the option on FBX relatively high and price the option on EUR/JPY relatively low.
B
Price the option on FBX relatively low and price the option on EUR/JPY relatively low.
C
Price the option on FBX relatively low and price the option on EUR/JPY relatively high.
D
Price the option on FBX relatively high and price the option on EUR/JPY relatively high.