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FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

A risk analyst models the joint behavior of two assets by letting each asset follow its own geometric Brownian motion, with the Brownian increments linked through a correlation parameter rho. Which statement best describes the role of rho in this bottom-up setup?

Rho is the instantaneous correlation between the Brownian motion increments of the two assets, so that dW1 dW2 equals rho times dt. It links the random shocks, not the drifts, volatilities, or the correlation of price levels.

  1. AIt sets the correlation between the Brownian increments (dW1, dW2), so that dW1 dW2 = rho dtCorrect
  2. BIt sets the correlation between the drift terms of the two assets only
  3. CIt equals the correlation between the asset price levels over any horizon
  4. DIt fixes the volatility of each asset's diffusion term

Explanation

In a correlated GBM model, the Wiener process increments satisfy E[dW1 dW2] = rho dt. This links the random shocks, not the drifts or volatilities. Correlation of price levels or of returns over finite horizons is approximately but not exactly rho, so the level-correlation option is wrong.

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