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

A one-year European call and put on a non-dividend stock share the same strike K and maturity. The put's implied volatility is 28%, and the call has the same strike. Using put-call parity, which implied volatility must the call have if both are priced consistently and the put is priced at the Black-Scholes-Merton price with 28% volatility?

The call must have an implied volatility of 28%. Put-call parity links European call and put prices at the same strike and maturity, and Black-Scholes-Merton prices satisfy parity at a single volatility, so both options share one implied volatility.

  1. A28%, because put-call parity requires the same implied volatility for European options with the same strike and maturityCorrect
  2. BLess than 28%, because calls always have lower implied volatility
  3. CMore than 28%, because calls carry the upside premium
  4. DIt cannot be determined without the dividend yield and interest rate

Explanation

Put-call parity holds irrespective of the model, so the call price equals the put price plus S0 minus K discounted. Since the Black-Scholes-Merton prices satisfy parity at a single volatility, the call and put at the same strike must share the same implied volatility. The interest rate and dividend are unnecessary for the conclusion because the stock pays no dividend and the same parameters are used in both prices.

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