FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches
A quant models correlation as a mean-reverting process: d(rho) = a*(m - rho)*dt + s*dW, with a = 2, long-run mean m = 0.50. Current correlation is 0.80, and volatility is ignored (deterministic drift only). Using a single small step dt = 0.25 in Euler discretisation, what is the correlation after the step?
The Euler step moves correlation by a times (m minus rho) times dt, which is 2 times minus 0.30 times 0.25, or minus 0.15. Correlation therefore falls from 0.80 to 0.65, moving toward the long-run mean of 0.50.
- A0.65Correct
- B0.75
- C0.35
- D0.95
Explanation
Drift = 2*(0.50-0.80)*0.25 = -0.15. New rho = 0.80 - 0.15 = 0.65. The 0.95 option has the wrong sign of the reversion; 0.75 uses a*dt=0.1 mistakenly; 0.35 doubles the adjustment.
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