Ornstein-Uhlenbeck (OU) Process

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. ...

Stochastic Approaches to Asset Price Analysis ArXiv ID: 2407.06745 “View on arXiv” Authors: Unknown Abstract In this project, we propose to explore the Kalman filter’s performance for estimating asset prices. We begin by introducing a stochastic mean-reverting processes, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman filter in detail, and its application with this model. After a demonstration of the Kalman filter on a simulated OU process and a discussion of maximum likelihood estimation (MLE) for estimating model parameters, we apply the Kalman filter with the OU process and trailing parameter estimation to real stock market data. We finish by proposing a simple day-trading algorithm using the Kalman filter with the OU process and backtest its performance using Apple’s stock price. We then move to the Heston model, a combination of Geometric Brownian Motion and the OU process. Maximum likelihood estimation is commonly used for Heston model parameter estimation, which results in very complex forms. Here we propose an alternative but easier way of parameter estimation, called the method of moments (MOM). After the derivation of these estimators, we again apply this method to real stock data to assess its performance. ...

End-to-End Policy Learning of a Statistical Arbitrage Autoencoder Architecture ArXiv ID: 2402.08233 “View on arXiv” Authors: Unknown Abstract In Statistical Arbitrage (StatArb), classical mean reversion trading strategies typically hinge on asset-pricing or PCA based models to identify the mean of a synthetic asset. Once such a (linear) model is identified, a separate mean reversion strategy is then devised to generate a trading signal. With a view of generalising such an approach and turning it truly data-driven, we study the utility of Autoencoder architectures in StatArb. As a first approach, we employ a standard Autoencoder trained on US stock returns to derive trading strategies based on the Ornstein-Uhlenbeck (OU) process. To further enhance this model, we take a policy-learning approach and embed the Autoencoder network into a neural network representation of a space of portfolio trading policies. This integration outputs portfolio allocations directly and is end-to-end trainable by backpropagation of the risk-adjusted returns of the neural policy. Our findings demonstrate that this innovative end-to-end policy learning approach not only simplifies the strategy development process, but also yields superior gross returns over its competitors illustrating the potential of end-to-end training over classical two-stage approaches. ...