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

A risk manager compares two volatility surfaces for an equity index, one before and one after a market sell-off. After the sell-off, short-dated implied volatilities rise sharply while long-dated volatilities rise only slightly, and the skew at short maturities steepens. Which interpretation and consequence is most appropriate for the manager's delta hedging of a short-dated option book using a sticky-strike versus sticky-delta assumption?

Short-dated volatility rising more than long-dated inverts the front end, and with a steep skew the correct delta depends on how the surface moves with spot. Under sticky-strike versus sticky-delta assumptions the volatility at a strike changes differently, so hedge ratios differ.

1. ATerm structure inverts at the front end, and the hedge ratio depends on how the surface moves with the index; under sticky-delta the volatility at a given strike changes as spot moves, so the model delta differs from the sticky-strike deltaCorrect
2. BThe surface is irrelevant to delta because delta depends only on spot and the risk-free rate
3. CInversion implies long-dated options are mispriced, so they should be sold regardless of the hedge
4. DSteeper skew means volatility is constant across strikes, so delta is unaffected