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FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces

A risk analyst compares market prices of European options on a stock with Black-Scholes prices computed using a single constant volatility. Which of the following is the defining feature of the implied volatility of an option?

Implied volatility is the volatility input that makes the Black-Scholes model price equal the observed market price of the option. It is backed out of option prices, unlike historical or GARCH volatility, which are estimated from past return data.

  1. AIt is the volatility that, when input into the Black-Scholes formula, reproduces the observed market price of the optionCorrect
  2. BIt is the standard deviation of historical daily returns annualized over the last 250 trading days
  3. CIt is the volatility forecast by a GARCH model fitted to the underlying's returns
  4. DIt is the average of the call and put payoffs divided by the strike price

Explanation

Implied volatility is found by inverting the Black-Scholes formula so the model price equals the market price. Historical and GARCH volatilities are estimates from past returns, not derived from option prices. The payoff-based option is not a volatility measure.

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