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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A European call on a non-dividend-paying stock trades in the market at a price below its Black-Scholes-Merton value computed with the trader's historical volatility of 30%. Holding other inputs fixed, which statement is correct about the implied volatility of this call?

Implied volatility is below 30%. The BSM call price rises monotonically with volatility, so a market price below the model value at 30% volatility means the volatility that reproduces the market price must be lower than 30%.

  1. AIt is greater than 30%
  2. BIt is less than 30%Correct
  3. CIt equals 30% because volatility is unobservable
  4. DIt cannot be determined without the option's delta

Explanation

The BSM call price increases monotonically with volatility. The market price is below the model price at 30%, so the volatility that equates model and market price must be lower than 30%. Delta is not needed.

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