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

Market prices of options on the same share and with the same expiry show implied volatilities that are higher for deep out-of-the-money puts than for at-the-money options. Which Black-Scholes assumption does this most directly contradict?

It contradicts the assumption of constant volatility with lognormal returns. Under Black-Scholes a single volatility would price options of all strikes, but a smile or skew shows the market allows for fatter tails or changing volatility.

  1. AInvestors are risk-neutral
  2. BConstant volatility, together with lognormally distributed returnsCorrect
  3. CThe option is European and exercisable only at expiry
  4. DThe share pays no dividends
  5. Short selling is permitted without restriction

Explanation

If Black-Scholes held exactly, one volatility would reproduce all strikes. A volatility smile or skew shows the market uses fatter tails or non-constant volatility than lognormal returns with constant sigma imply. Risk neutrality is a pricing device, not a testable assumption here.

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