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IAI Actuarial Core Principles · Economic Modelling · Stochastic models for security prices

Under the lognormal model for a share price, which of the following is a recognised limitation when compared with observed market data?

A key limitation is that the lognormal model assumes constant volatility and normally distributed log returns, so it cannot capture the fat tails and volatility clustering seen in actual market returns. Extreme events are therefore underestimated.

  1. AIt allows prices to fall below zero
  2. BIt assumes constant volatility and cannot reproduce fat tails in returnsCorrect
  3. CIt assumes returns in non-overlapping periods are correlated
  4. DIt gives a mean price that decreases as μ rises
  5. It requires the price to be normally distributed

Explanation

The model assumes constant σ and normal log returns, so it underestimates extreme moves and volatility clustering seen in real data. Prices cannot be negative under it, and its increments are independent, not correlated. The mean rises with μ.

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