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

A trader holds a long position in a 3-month out-of-the-money index put struck at 90% of spot. The trader prices it with the at-the-money implied volatility of 20%, while the market quotes 26% for that strike. Assuming the put's vega is 0.05 per volatility point per unit, what is the approximate mispricing per unit of the put relative to the market quote?

The put is underpriced by about 0.30 per unit. The strike-specific implied volatility is 6 points above the at-the-money level, and with vega of 0.05 per point the price gap is 6 times 0.05, or 0.30, with the flat-volatility price too low.

  1. A0.30 too lowCorrect
  2. B0.30 too high
  3. C0.05 too low
  4. D1.20 too low

Explanation

Volatility difference is 26% minus 20% = 6 points. Price difference is about 6 x 0.05 = 0.30. Using the lower at-the-money volatility understates the put value, so the model price is 0.30 too low. Ignoring the skew is the error.

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