For 1-year SPX options, we observe that the 25-delta put implied volatility is at 45%,...
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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) fat tailed, (d) thin tailed"
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