FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
A risk analyst compares two volatility estimates for an equity index. The historical estimate uses 250 daily returns, each weighted equally. The implied estimate is backed out from the market price of one-month at-the-money options using the Black-Scholes-Merton model. Which statement best describes a key difference between the two?
Implied volatility is forward-looking because it is extracted from current option prices and reflects market expectations, whereas equal-weighted historical volatility relies only on past returns and responds slowly to new information. Implied volatility is not guaranteed to be an unbiased forecast of realized volatility.
- AImplied volatility is forward-looking and reflects market expectations, while equal-weighted historical volatility is backward-looking and slow to react to new informationCorrect
- BImplied volatility is computed from past returns only, while historical volatility is observed directly in option prices
- CHistorical volatility reflects the market's risk premium for volatility, while implied volatility is free of any model assumptions
- DImplied volatility is always an unbiased forecast of realized volatility, while historical volatility always overstates it
Explanation
Implied volatility is obtained by inverting an option pricing model using current option prices, so it embeds market expectations about the future. Equal-weighted historical volatility uses only past returns and adjusts slowly. The claim that implied volatility is always unbiased is wrong; it often exceeds realized volatility because of a volatility risk premium.
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