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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

Over the past year, equity index options with a strike 10% below spot have had implied volatilities of 28%, while at-the-money options have had 20%. This pattern is best described as:

This is a volatility skew: implied volatility is higher for low strikes than for at-the-money options. It contradicts the constant-volatility assumption of Black-Scholes-Merton and is typical of equity index options, where downside protection is in high demand.

  1. AA volatility skew, inconsistent with constant volatility in the Black-Scholes-Merton modelCorrect
  2. BA flat term structure, consistent with the Black-Scholes-Merton model
  3. CEvidence that historical volatility is constant over time
  4. DA volatility smile that is symmetric around the at-the-money strike

Explanation

Implied volatility falling as strike rises is a skew (smirk), typical of equity index options due to crash fear and leverage. Black-Scholes-Merton assumes one constant volatility, so differing implied volatilities across strikes contradict it. The pattern is not symmetric.

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