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

A desk prices a European put with a strike of 90 using flat 20% Black-Scholes volatility. The market quotes this put at an implied volatility of 26%. Holding all else equal, which conclusion is correct about the market price versus the flat-volatility price?

The market price is higher than the flat 20% price. European option values rise with volatility (positive vega), so a 26% implied volatility implies a greater premium, reflecting the skew that makes low-strike puts expensive relative to Black-Scholes.

  1. AThe market price is higher, because put value increases with volatilityCorrect
  2. BThe market price is lower, because put value decreases with volatility
  3. CThe prices are equal, because strikes do not affect volatility
  4. DThe market price is higher only if interest rates are zero

Explanation

Option vega is positive for European puts and calls, so a higher volatility input gives a higher price. A 26% implied volatility therefore gives a higher price than a 20% input. Strike dependence of implied volatility is exactly what the skew captures, and the conclusion does not depend on rates.

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