CIR Mean-Reversion Trading: Fitting and Optimal Entry and Exit

Summary

This document explains how to model a mean-reverting portfolio with a Cox-Ingersoll-Ross (CIR) process, whose volatility scales with the square root of its value. It describes fitting the process by maximum likelihood and selecting portfolio weights to maximize the fitted likelihood. The model’s long-run mean, reversion speed, and volatility determine its dynamics.

For a single entry and exit, the optimal-stopping framework chooses liquidation and entry thresholds by solving equations derived from the process’s differential generator. It accounts for transaction costs and discounting, and discusses adding a stop-loss. The optimal-switching framework considers repeated trades and gives conditions for when re-entry is worthwhile. The document outlines software functions for fitting, calculating levels, plotting, and displaying model statistics, but provides no empirical trading results. Its guidance relies on CIR dynamics and the cited mathematical treatment; the excerpt does not establish that market portfolios follow this process or that estimated thresholds will perform out of sample.

Key ideas

• The CIR process models a positive portfolio value with mean reversion and value-dependent volatility.
• Maximum likelihood estimates the process parameters, while portfolio weights are selected to improve the fitted likelihood.
• Optimal stopping selects entry and liquidation thresholds for one trade, incorporating discounting and transaction costs.
• Optimal switching evaluates repeated entry and exit cycles and supplies conditions for whether re-entry is worthwhile.
• The described framework is model-dependent, and the document provides no empirical validation of trading performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.