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Correlated Brownian motions

Two motions share a common shock: the second is ρ times the first plus an independent part, the Cholesky factor of the correlation matrix.

Parameters

Correlation (ρ)0.70

-0.990.99

Steps300

501000

Random seed: 7

Metrics

Target correlation

0.70

Empirical correlation

0.69

Second motion

0.70·Z₁ + 0.71·Z₂

The paired paths

W₁W₂

300 increment pairs (ΔW₁, ΔW₂) with the line ΔW₂ = ρ·ΔW₁