PMCC-001: method and limits

Return to findings and rerunnable experiment

Paired control and accounting

Both option strategies hold exactly the same one-contract long call and execute identical long-call rolls. Only PMCC sells short calls. Terminal overlay contribution equals net short-option P/L plus the difference in cash interest and borrowing charges. Every run checks this identity to within $0.000001. Open options are marked at the final observation; no final liquidation fee is assumed.

Pricing, timing and data

European Black–Scholes calls include continuous dividend yield. Rolling volatility uses the latest 21 historical adjusted log returns available at each close, annualized with 252 sessions, bounded to 7–80%, then multiplied by one plus the IV premium. History preceding the selected start is retained. Transactions at a session close use information through that close; they do not model next-session execution or intraday slippage.

The adjusted-return path is converted to a synthetic price-only proxy by subtracting q × elapsed calendar days / 365 from each log return. This is not a recovery of actual historical prices. Each study begins at $100. The stock reference compounds unmodified adjusted returns. Dividend rates are constant assumptions, and options use a constant risk-free rate.

Expiration is the final available market session on or before the target calendar date, with exact calendar-date expiry retained beyond the data horizon for final marking. DTE declines by actual elapsed calendar days. Short calls are cash-settled for intrinsic value plus a fee. New short strikes are constrained to be at least 1% above the long strike, so achieved short delta may be below the target. If a long roll raises its strike above the short strike, the short is closed and replaced. There is no discretionary early profit-taking.

Theta diagnostic

Before each underlying-price update, each option is repriced at its shorter remaining maturity while holding the preceding spot and volatility fixed. Summing these differences provides a time-only repricing diagnostic. It is path-dependent and does not by itself reconcile total P/L; interactions with price and volatility are not separately attributed. Deep-ITM dividend-paying calls need not exhibit negative theta under every parameter setting.

Interpretation and limitations

• Historical adjusted-return record ending 2026-08-14; option price path is a constant-yield-adjusted synthetic proxy normalized to 100 at each start.
• One contract maintained; exposure is not rebalanced to the all-stock comparator. Long-only is the causal control within the model.
• Black-Scholes European-style prices, no archived quotes, skew, slippage, early assignment, taxes or broker margin constraints.
• Expiration uses last observed session on or before target calendar date; daily closes cannot reproduce intraday fills.
• Borrowing is charged and disclosed; any nonpositive strategy equity rejects a configuration.
• Annual cash, borrowing and dividend assumptions are constant scenarios, not historical rate estimates.
• The theta diagnostic holds prior spot and volatility fixed. It is not an independently earned return or exact additive attribution.

Positive cash compounds continuously at 4%, negative cash at 7%, over actual elapsed days. Broker collateral rules and position limits are not modeled. Runs stop with an error if either strategy has nonpositive equity; failed configurations are recorded, not silently discarded.

Reproduction

From the extracted study folder run node test.mjs and node execute.mjs. The source package includes both data files, engine, frozen protocol, all results and SHA-256 fingerprints. Then run node build-report.mjs to rebuild this report and archive entry. Browser runs execute the same engine. No AI, brokerage or market-data API calls are made.

Mark L. Morrissey · PMCC-001 · Executed 2026-09-22. Model research, not investment advice.