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

A risk analyst compares two volatility estimates for an equity index. The 30-day historical volatility computed from daily returns is 14%, while the volatility implied by at-the-money one-month index options is 19%. Which statement is the most appropriate interpretation?

Implied volatility is forward-looking, derived from current option prices, and can exceed historical volatility because it includes a premium for volatility risk. The two measures need not match, so a gap does not mean either estimate is wrong or the model was misapplied.

  1. AImplied volatility is backward-looking and so reflects only the past 30 days of returns
  2. BImplied volatility reflects the market's forward-looking expectation, and may include a risk premium for bearing volatility riskCorrect
  3. CHistorical volatility must be wrong because it is lower than implied volatility
  4. DThe gap shows the option pricing model has been misapplied, since the two measures must be equal

Explanation

Implied volatility is backed out of option prices and is forward-looking. It often exceeds subsequently realized volatility because option sellers demand a volatility risk premium. Historical volatility is backward-looking, and the two need not be equal.

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