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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

Equity index options show implied volatility much higher for low-strike puts than for high-strike calls (a negative skew). Which explanation is most consistent with this pattern?

The skew is consistent with demand for downside protection and a return distribution with a fatter left tail than the lognormal. Both raise the price of low-strike puts, which pushes up their implied volatility relative to high-strike calls.

  1. AReturns are lognormal with constant volatility
  2. BInvestors pay a premium for downside protection and the real return distribution has a fatter left tail than the lognormalCorrect
  3. CThe risk-free rate is negative
  4. DCall options are always more liquid than puts
  5. Dividends are paid continuously

Explanation

Demand for portfolio insurance bids up low-strike puts, and empirical returns show negative skewness and excess kurtosis relative to lognormal. Both imply higher implied volatility at low strikes. Constant-volatility lognormal returns would give a flat profile.

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