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

An index is at 4,000. A trader notes that implied volatility is 24% for the 3,600 strike and 16% for the 4,400 strike, both with three months to expiry. If the trader instead used the at-the-money volatility of 20% for both options, which conclusion is correct for the trader's valuation?

Using 20% for both undervalues the 3,600 put, since the market implies 24%, and overvalues the 4,400 call, since the market implies 16%. Option prices rise with volatility, so using too low a volatility understates value and using too high a volatility overstates it.

  1. AThe 3,600 put would be undervalued and the 4,400 call would be overvaluedCorrect
  2. BThe 3,600 put would be overvalued and the 4,400 call undervalued
  3. CBoth options would be undervalued
  4. DBoth options would be overvalued

Explanation

The market's implied volatility for the 3,600 strike is 24%, above the 20% used, so valuing it at 20% gives a lower price: undervalued. For the 4,400 strike the market volatility is 16%, below 20%, so the 20% valuation gives too high a price: overvalued. Option B reverses the direction.

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