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Answer: Historical volatility is calculated by taking the standard deviation of returns, while implied volatility is the volatility that equates the option price produced by the Black-Scholes-Merton model with the observed market price of the option.
**D is correct.** The volatility of an asset is usually measured using the standard deviation of the returns. Furthermore, the value of σ that equates the observed call option price with the value computed via the BSM formula for the call option price is known as the implied volatility. **A is incorrect.** Implied volatility is an annual figure by construction, so no transformation is necessary. Variance rate can be scaled to the desired time horizon. **B is incorrect.** The variance rate scales linearly with time. Historical volatility, on the other hand, scales with the square root of the holding period. **C is incorrect.** These statements cannot be concluded as historical volatility may or may not be less than the implied volatility.
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An intern at a hedge fund is reviewing the different measures of volatility that are used in the firm's risk analytics framework for option portfolios. The intern compares the key features of historical volatility, implied volatility, and variance rate. Which of the following is a correct conclusion for the analyst to make?
A
Implied volatility needs to be annualized by scaling between time horizons, while the variance rate is an annual value by construction.
B
The variance rate scales with the square root of the holding period, while historical volatility scales linearly with time.
C
Historical volatility is less than implied volatility, while the variance rate is greater than historical volatility.
D
Historical volatility is calculated by taking the standard deviation of returns, while implied volatility is the volatility that equates the option price produced by the Black-Scholes-Merton model with the observed market price of the option.