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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

The implied volatilities of equity index options with the same maturity are 28% for a 90% strike, 22% for a 100% strike and 20% for a 110% strike. Which interpretation is most appropriate?

This is a volatility skew. Implied volatility declines as strike rises, which is typical of equity index options and reflects greater perceived probability of large downward moves than the lognormal assumption in Black-Scholes-Merton implies. It contradicts constant volatility across strikes and is not a symmetric smile.

  1. AThe pattern is a volatility skew, indicating the market assigns higher probability to large downward moves than a lognormal distribution impliesCorrect
  2. BThe pattern shows that Black-Scholes-Merton holds exactly, since volatility is constant across strikes
  3. CThe pattern is a volatility smile symmetric around the money, implying fat right tails
  4. DThe pattern implies options at the 110% strike are overpriced relative to the 90% strike

Explanation

Implied volatility falls as strike rises, a downward-sloping skew typical of equity indices. It indicates a heavier left tail than lognormal, with demand for downside puts. Constant volatility across strikes would be required for BSM to hold, and the pattern is not symmetric.

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