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

A trader notes that a 3-month European call on a non-dividend-paying stock has a market price that is below the Black-Scholes price computed with the analyst's 25% volatility estimate, with all other inputs identical. Which conclusion is correct?

The implied volatility is below 25%. Black-Scholes option prices rise monotonically with volatility because vega is positive, so a market price lower than the model price at 25% requires a lower volatility input to reproduce it.

  1. AThe option's implied volatility is below 25%, because option price is increasing in volatilityCorrect
  2. BThe option's implied volatility is above 25%, because the market price is too low
  3. CThe implied volatility equals 25%, because other inputs match
  4. DNo conclusion is possible, because the call vega can be negative

Explanation

A European call price on a non-dividend stock increases monotonically in volatility (vega is positive). Since the market price is below the model price at 25%, the volatility that matches the market price must be lower than 25%. Vega is never negative for a standard European option.

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