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16 January, 10:25

For 1-year SPX options, we observe that the 25-delta put implied volatility is at 45%, the 50-delta call implied volatility is at 30%, the 25-delta call implied volatility is at 35%. These observations suggest that the option-implied SPX 1-year return risk-neutral distribution is (a) normally distributed, (b) positively skewed, (c) thin tailed, (d) negatively skewed

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  1. 16 January, 10:28
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    Option B, positively skewed, is the right answer.

    Explanation:

    A positive-skewed distribution generally has a long right or positive tail. The positive-skew distributions are also known as the Right-skewed distribution. The main reason behind calling this a positive-skew is that this skew has a long tail in the positive direction on the number line.

    In the given question, positively-skewed implies to one-year return risk-neutral distribution, as the delta put raises, the volatility decreases but not in the same proportion. In such a condition, the median will be less than the mean. Therefore, it will be Right-Skewed or Positively Skewed Distribution.
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