1. Mathematical Foundations of Statistical Arbitrage
Statistical arbitrage leverages mathematical divergence models to identify temporary mispricings between historically correlated financial instruments. Rather than assuming deterministic parity, our models model residual spreads as mean-reverting Ornstein-Uhlenbeck (OU) diffusion processes.
2. Co-Integration and Johansen Testing
Pairwise asset selection requires statistical verification that linear combinations of integrated time series exhibit stationarity. We utilize the Johansen multi-variate test to identify the maximum likelihood estimators of co-integrating vectors across spot, futures, and foreign exchange liquidity pools.
dXt = θ(μ - Xt)dt + σdWt
Where θ defines the mean-reversion speed, μ is the long-term equilibrium spread level, and Wt represents a standard Wiener process. Volatility thresholds trigger automated signal generation whenever the z-score exceeds parameterized institutional tolerance bounds.
3. Risk Mitigation & Execution Feasibility
Real-world algorithmic deployment necessitates modeling borrow rates, market impact, and venue latency. CryptGlobal’s backtesting sandbox simulates execution under stress regimes with real tick-level historical data to guard against regime shift risks.
