FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A risk analyst compares the lognormal distribution assumed by Black-Scholes with the distribution implied by equity option prices. Equity index options typically show implied volatility falling as strike rises. Relative to the lognormal distribution, what does this imply about the risk-neutral distribution of the index?
A downward-sloping equity skew implies a heavier left tail and a lighter right tail than lognormal, because low-strike options carry higher implied volatility, signalling greater probability of large price declines than Black-Scholes assumes.
- AA heavier left tail and a lighter right tailCorrect
- BA heavier right tail and a lighter left tail
- CEqually heavy tails on both sides
- DThinner tails on both sides
Explanation
A downward-sloping skew means low-strike options (puts) are priced with higher implied volatility than lognormal. This puts more probability on large declines, so the left tail is heavier. The right tail is lighter because high-strike options have lower implied volatility. The right-tail-heavy option is the pattern for currencies or commodities with opposite skew.
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