Trading the Eigenvalues: Statistical Arbitrage via the Implied Generator

We develop a systematic trading framework based on the implied generator — the Fokker--Planck generator matrix \(M\) recovered from option prices without parametric assumptions. The core insight is not that markets misprice (they don't), but that the implied generator reveals the structure of the market's belief in spectral form: eigenvalues encode mean reversion speed, smile dynamics rate, and tail decay. Five trading strategies exploit this structure: (1) illiquid maturity pricing — \(M\) interpolates between liquid maturities more accurately than per-slice models, enabling trading inside wide bid-ask spreads; (2) calendar spread relative value — \(M\)'s temporal consistency detects inter-maturity mispricing caused by per-slice calibration; (3) hedge improvement — \(M\)'s analytical Greeks reduce hedging P\&L variance by an estimated 1--3\% compared to Heston-calibrated Greeks; (4) eigenvalue regime detection — daily tracking of \(\lambda_1(M)\) provides a leading indicator of volatility regime shifts, unavailable from any price or implied vol directly; (5) exotic--vanilla consistency — the killed generator from \(M\) prices barriers consistently with vanillas, detecting mispricing in exotic desks. On a synthetic backtest, the smile-mispricing strategy produces a Sharpe ratio of 0.91 on 29 trades with 100\% win rate against a Heston-calibrated counterparty. The implied generator is not an alpha source in itself — it is a lens that reveals tradeable structure in the option market's collective belief.