📊 Mean Reversion Trading Strategy using Ornstein-Uhlenbeck Process

A quantitative trading strategy utilizing the Ornstein-Uhlenbeck process to identify mean-reverting opportunities between S&P500 (SPY), optimizing trade execution for profitable arbitrage when the market falls out of conventional sense.

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📝 Description

This projects attempts to find market arbitrage especially when the market enters into states of disorientations using the Ornstein-Uhlenbeck (OU) stochastic differential equation. The OU price generated by the equation creates an artificial price target to exit when the stock approaches the OU price.

Key Highlights:

• Statistical modeling of ETF/Currencies.
• Signal generation based on mean-reverting properties.
• Backtesting framework to evaluate performance.
• Integration with live trading platforms (Interactive Brokers API).

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⚙️ Mathematical Framework

The relationship between securities' prices and its conventional market sentiment is modeled using the Ornstein-Uhlenbeck (OU) Process:

$$ dX_t = \theta (\mu - X_t) dt + \sigma dW_t $$

Where:

• $X_t$: Current price of security.
• $\theta$: Speed of mean reversion where $\theta$ = ln(0.5)/ln(b)
• $\mu$: Long-term mean of the spread.
• $\sigma$: Volatility of the spread.
• $dW_t$: Brownian motion term.

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