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

A market maker is short a large book of out-of-the-money equity puts and hedges delta daily. The market moves to a sharper skew without the underlying price changing. Which Greek exposure is most directly responsible for the mark-to-market change due to a change in the shape of the volatility smile rather than the spot move?

Vega exposure, measured across strikes, drives the loss. With spot unchanged, a steeper skew raises implied volatility at the low strikes where the puts sit, increasing their value and hurting the short position. Gamma, theta and rho do not capture a change in smile shape.

  1. ATheta
  2. BVega, including exposure to skew-related changes in implied volatility at different strikesCorrect
  3. CRho
  4. DGamma only

Explanation

Holding spot constant, a change in implied volatility at various strikes changes option values through vega at those strikes. A skew steepening raises low-strike volatilities, hurting short puts. Gamma relates to spot moves, theta to time and rho to rates.

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