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

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  • SeungJae Hwang

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.

Suggested Citation

  • SeungJae Hwang, 2025. "A Mean-Reverting Model of Exchange Rate Risk Premium Using Ornstein-Uhlenbeck Dynamics," Papers 2504.06028, arXiv.org.
    • Handle: RePEc:arx:papers:2504.06028
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    File URL: http://arxiv.org/pdf/2504.06028
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