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

An analyst notes that over several years, implied volatility from index options has on average been higher than the subsequently realized volatility of the index. Which explanation is most consistent with this observation?

Implied volatility has tended to exceed realized volatility because option prices include a volatility risk premium: sellers of options require compensation for bearing the risk that volatility spikes in bad markets. Implied volatility comes from option prices, not past returns, and the Black-Scholes-Merton model assumes constant volatility.

  1. AOption sellers demand compensation for bearing volatility risk, creating a volatility risk premium embedded in option pricesCorrect
  2. BHistorical volatility is calculated with too many observations, so realized volatility is always understated
  3. CThe Black-Scholes-Merton model assumes volatility is stochastic, which inflates implied volatility
  4. DImplied volatility is derived from the underlying's past returns, which include crisis periods

Explanation

Implied volatility is extracted from option prices, which include a premium for the risk that volatility spikes, typically when investors are hurting. This pushes implied above realized on average. BSM assumes constant, not stochastic, volatility, and implied volatility is not computed from past returns.

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