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Mean reversion: Ornstein–Uhlenbeck

A rate pulled back towards a long-run level θ at speed κ while noise keeps pushing it away. Paths settle into a band of width σ/√(2κ).

Parameters

Reversion speed (κ)1.5

0.16

Long-run level (θ)3.0%

-0.020.1

Volatility (σ)2.0%

0.0050.06

Start (X₀)1.0%

-0.050.1

Random seed: 7

Metrics

Half-life

0.46 yr

Stationary band width

±1.15%

Paths ever below 0

29%

Below 0 at T (exact)

0.3% (0.5%)

600 rate paths with the expected path, the θ ± band and the half-life

Distribution at T = 5 (rate in %) against the exact normal law