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

Which is a recognised limitation of modelling an equity index with GBM with constant μ and σ?

A key weakness of GBM is its constant volatility and normally distributed log returns, which cannot reproduce the volatility clustering and fat tails seen in real market data. It does keep prices positive and has independent returns.

  1. AIt permits negative index values
  2. BIt cannot produce any positive expected return
  3. CIt assumes constant volatility, so it cannot reproduce volatility clustering or fat tails seen in observed returnsCorrect
  4. DIt makes log returns correlated across non-overlapping periods
  5. It requires the index to be mean-reverting

Explanation

GBM has independent normal log returns with constant volatility, so it cannot capture volatility clustering or heavy tails seen in real data. It does keep prices positive, allows positive returns, and has independent increments, with no mean reversion.

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