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

A risk analyst compares implied volatilities of EUR/USD options across strikes and observes a U-shaped pattern, with out-of-the-money calls and puts both having higher implied volatility than at-the-money options. Which feature of the underlying exchange rate distribution, relative to the lognormal assumption, best explains this foreign currency smile?

The U-shaped smile arises because the exchange rate distribution has fatter tails than the lognormal distribution on both sides. Extreme moves in either direction are more likely than Black-Scholes assumes, so out-of-the-money calls and puts are priced with higher implied volatility than at-the-money options.

  1. AThe exchange rate has fatter tails than a lognormal distribution, with both extreme moves more likelyCorrect
  2. BThe exchange rate has a thinner right tail and a heavier left tail than lognormal
  3. CThe exchange rate volatility is constant and the distribution is exactly lognormal
  4. DThe exchange rate has thinner tails than lognormal, with extreme moves less likely

Explanation

A symmetric U-shaped smile in currency options indicates that both tails of the exchange rate distribution are heavier than lognormal. Heavier tails raise the value of deep out-of-the-money options and so raise their implied volatility. A left-heavy and right-thin distribution would produce a skew, not a smile.

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