FRM Part II · FRM Exam Part II · Volatility Smiles and Volatility Surfaces
A risk manager uses a simple practitioner approach in which implied volatility is modeled as a quadratic function of strike, fitted to market quotes, rather than a structural model. Which is the main advantage of this approach and the main concern?
A quadratic fit of implied volatility to strike is quick and matches observed quotes well, making it practical for interpolation. Its drawbacks are that it gives no economic explanation, does not guarantee absence of arbitrage such as negative implied densities, and can extrapolate poorly to extreme strikes.
- AIt guarantees no-arbitrage and explains why the smile exists
- BIt fits observed quotes quickly, but may imply arbitrage opportunities or poor extrapolation outside the fitted rangeCorrect
- CIt forces the smile to be flat, but is theoretically rigorous
- DIt captures jump risk explicitly, but cannot fit short maturities
Explanation
Ad hoc functional fits to strikes are easy and match quotes closely, which is useful for pricing and interpolation. They offer no economic explanation and do not ensure no-arbitrage, for example negative implied densities, and extrapolation to extreme strikes can be unreliable. Hence option B.
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