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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A trader observes that implied volatilities for equity index options are higher for low strikes than for high strikes of the same maturity. Which interpretation is most consistent with this pattern relative to the Black-Scholes-Merton assumptions?

The skew implies the market puts more probability on large downward moves than the lognormal distribution does, meaning a fatter left tail. Low-strike puts are priced with higher implied volatility to reflect crash risk and leverage effects.

  1. AThe market assigns a fatter left tail than the lognormal distribution impliesCorrect
  2. BThe market assigns a thinner left tail than the lognormal distribution implies
  3. CVolatility is constant, and the pattern reflects dividend yield differences
  4. DThe market expects returns to be normally distributed with higher variance

Explanation

A downward-sloping skew means out-of-the-money puts (low strikes) are priced with higher volatility, implying greater probability of large declines than lognormal. A thinner left tail would produce lower implied volatility at low strikes. Constant volatility would give a flat smile.

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