A Mean-Reverting Model of Exchange Rate Risk Premium Using Ornstein-Uhlenbeck Dynamics

ArXiv ID: 2504.06028 “View on arXiv”

Authors: Unknown

Abstract

This paper examines the empirical failure of uncovered interest parity (UIP) and proposes a structural explanation based on a mean-reverting risk premium. We define a realized premium as the deviation between observed exchange rate returns and the interest rate differential, and demonstrate its strong mean-reverting behavior across multiple horizons. Motivated by this pattern, we model the risk premium using an Ornstein-Uhlenbeck (OU) process embedded within a stochastic differential equation for the exchange rate. Our model yields closed-form approximations for future exchange rate distributions, which we evaluate using coverage-based backtesting. Applied to USD/KRW data from 2010 to 2025, the model shows strong predictive performance at both short-term and long-term horizons, while underperforming at intermediate (3-month) horizons and showing conservative behavior in the tails of long-term forecasts. These results suggest that exchange rate deviations from UIP may reflect structured, forecastable dynamics rather than pure noise, and point to future modeling improvements via regime-switching or time-varying volatility.

Keywords: Uncovered Interest Parity (UIP), Ornstein-Uhlenbeck (OU) Process, Risk Premium, Stochastic Differential Equation (SDE), Mean Reversion, Foreign Exchange (FX)

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced stochastic calculus (Ornstein-Uhlenbeck SDEs, derived closed-form approximations) and rigorous statistical estimation, demonstrating high mathematical density. It is empirically robust, featuring a detailed backtesting framework with coverage-based metrics, real financial data (USD/KRW 2010-2025), and quantitative performance evaluation across multiple horizons.
  flowchart TD
    A["Research Goal: Explain UIP failure<br>via Mean-Reverting Risk Premium"] --> B["Data: USD/KRW 2010-2025"]
    B --> C["Methodology: Calculate Realized Premium<br>UIP Deviation = FX Return - Interest Diff"]
    C --> D["Modeling: Fit Ornstein-Uhlenbeck OU Process<br>to Premium Dynamics"]
    D --> E["Computational Process: Derive Closed-Form<br>Future Exchange Rate Distributions"]
    E --> F["Validation: Coverage-Based Backtesting<br>across Short, Medium, Long Horizons"]
    F --> G["Key Outcomes: Strong predictive power at<br>short/long horizons; 3-month underperformance"]
    F --> H["Implication: Structured, forecastable<br>dynamics vs. pure noise"]