FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
According to the standard explanation of foreign currency smiles, which two factors cause the exchange rate's risk-neutral distribution to deviate from lognormal and produce the smile?
The smile is caused by non-constant (stochastic) volatility and by jumps in the exchange rate, often triggered by central bank interventions. Both generate fatter tails than lognormal. These effects produce higher implied volatilities for out-of-the-money options, with the relative importance depending on option maturity.
- AFixed interest rate differentials and constant volatility
- BDividend yield uncertainty and early exercise of American options
- CStochastic volatility and the presence of jumps in the exchange rateCorrect
- DBid-ask spreads and low trading volume in at-the-money options
Explanation
The volatility of an exchange rate is not constant, and the rate sometimes jumps, typically due to central bank actions. Both effects create fat tails. Stochastic volatility has a stronger effect on long-dated options, while jumps matter more for short-dated ones.
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