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Ornstein-Uhlenbeck Process — mean reversion for pairs trading

quant.dhawan · 2026-03-12T14:01:24.000Z · in Quant & Trading
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100k ft — What is this?

Ornstein-Uhlenbeck Process — mean reversion for pairs trading
techniqueA-tier

50k ft — Why care?

Simulates the OU process showing mean reversion dynamics with theta (reversion speed), mu (equilibrium), and sigma (noise). Core model for pairs trading, interest rate spreads, and volatility signals in quantitative finance.
finance/tradingquantstochastic-processes

10k ft — Key takeaways

• OU process models mean-reverting behavior • Key params: theta (speed), mu (mean), sigma (noise) • Applied to pairs trading and rate spreads

5k ft — Tools & techniques

(no tools tagged) Mean Reversion, Pairs Trading, Stochastic Differential Equations, algorithmic trading, mean reversion

1k ft — Deep-dive / try it

Everything returns to the mean eventually. 📉📈 ​This is the Ornstein-Uhlenbeck (OU) process in action. While most retail traders chase trends, quants look for the "elasticity" of the market. ​In this simulation: ​Theta: The speed of reversion. How fast the price "snaps back" to the mean. ​Mu: The long-term equilibrium level (the magnet). ​Sigma: The volatility or "noise" around that path. ​In quantitative trading, we use this to model pairs trading, interest rate spreads, and volatility signatures. When the price gets too far from mu, the probability of a reversal increases. Comment "OU" to get free code repo to test the convergence on your data. 🚨 jiyan_todema   16w Setting volatility at 0.55? That’s quite aggressive
ornstein-uhlenbeck
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Collection: Quant & Trading