Optimal mean-reverting portfolio construction using Ornstein-Uhlenbeck process and maximum likelihood estimation method
The Ornstein-Uhlenbeck process is a stochastic process that has a tendency to drift towards its mean function. In the financial markets, the investors can observe assets prices reverting back to their long-run mean. Other examples of mean-reversion are visible in the dynamics of the rate and volatility, which are both fundamental subjects that are extensively researched in finance.
The first step of pairs trading is the identification of two highly co-moving assets. The previous article studied the application of OPTICS in pairs selection (Moraes Sarmento, Simão et. al. 2020) while introducing a rule-based approach, including the Hurst Exponent to ensure that the time-series of the spread is mean-reverting.
Once the mean-reverting spreads are chosen, a strategy has to be developed to determine the entry (exit) level to open (close) positions. In their paper, Tim Leung and Xin Li study the optimal timing of trades while considering the transaction costs, under the Ornstein-Uhlenbeck model. This article focuses on how the OU model and the MLE method are coupled to create the optimal portfolio.
Summary
- Ornstein-Uhlenbeck process
