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

A trader observes that a European call with strike 100 on a non-dividend-paying stock trades at a price that implies a volatility of 24% in the Black-Scholes model. Which statement about this implied volatility is correct?

Implied volatility is the volatility input that makes the Black-Scholes price equal the observed market price of the option. It is found by numerically inverting the formula, and it is not a historical or model-forecast volatility.

  1. AIt is the volatility that, when input into Black-Scholes, reproduces the observed market priceCorrect
  2. BIt is the historical standard deviation of the stock's returns over the option's life
  3. CIt is the volatility forecast by a GARCH model fitted to the stock
  4. DIt is the average of the volatilities of all options on the stock

Explanation

Implied volatility is obtained by inverting the Black-Scholes formula so the model price equals the market price. It is not a historical or GARCH estimate. It is specific to the option's strike and maturity, not an average across options.

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