Implicit Autocorrelation Diversification in Mean Reverting Processes

Introduction: Since the Morris review (2004) in the UK, and the MAAA/SOA/CAS ESGs towards the turn of the century, mean-reverting stochastic processes have been widely used to model inflation, interest rates, and other macroeconomic risk drivers in actuarial cashflow projections and financial risk models. In most practical implementations, autocorrelation is seldomly looked at and assumed to be flat. However, this is only asymptotically valid and can conceal a transient implicit diversification effect at finite horizons.

Methods: Looking at the class of mean-reverting diffusions based on Ornstein–Uhlenbeck specification (Vasicek, CIR, Hull–White), where finite-horizon lag-Δ autocorrelation is available in closed form, this paper aims to prove monotonic convergence to the stationary limit and analyze sensitivity to mean-reversion speed and horizon length. For practical materiality, Monte Carlo experiments across parameter grids for mean reversion and volatility on two representative use cases have been designed: inflation-linked liability cashflows and interest-rate-driven discounting distributions, comparing simulations with two stationary-imposition implementations (assuming a deterministic start different from the reverted mean): (i) empirical copula reordering of existing simulated paths and (ii) recursive reconstruction with a fixed flat-ρ target

Results: Across mean-reverting specifications, finite-horizon autocorrelation exhibits a pre-stationary term structure that converges to the long-run lag structure. In the Ornstein–Uhlenbeck benchmark with κ>0, the finite-horizon autocorrelation is increasing in t, and is independent of the initial level and reversion direction. Relative to stationary assumptions, early-horizon paths display weaker serial dependence and therefore stronger implicit diversification, leading to potentially material differences in aggregate variance and tail-risk metrics, especially for slow mean reversion and short-to-medium horizons.

Conclusions: Pre-stationary autocorrelation should be treated as an explicit modelling assumption in mean-reverting models. For deterministic starts, practical stationary-imposition overlays described before are shown and benchmarked against the baseline. This framework makes diversification effects measurable and provides a practical decision toolkit for model developers and validators.