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

A trader notices that an out-of-the-money put on a stock is quoted with an implied volatility well below that of neighbouring strikes, producing a non-convex call price curve across strikes. Which conclusion is most appropriate?

A price curve that is not convex in strike implies a negative implied density, so a butterfly spread would cost less than zero while paying off nonnegative amounts. This is an arbitrage opportunity rather than a legitimate skew effect, and the cheap option is the one mispriced.

  1. AThe quote is consistent with a skew and offers no opportunity
  2. BA butterfly spread would have negative cost, indicating an arbitrage opportunityCorrect
  3. CThe implied distribution has fat tails, so the option is correctly priced
  4. DThe put is overpriced relative to neighbouring strikes

Explanation

Absence of arbitrage requires call prices to be convex in strike, which equals a nonnegative implied density. A convexity violation means a butterfly spread has negative cost yet a nonnegative payoff, so it is an arbitrage. A low implied volatility means the option is cheap, not overpriced.

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