What the numbers are, and what they are not

The language model receives your thesis, the ticker's live spot, and the as-of date. It returns a constrained schema — not prose — containing an objective and a set of branches. Each branch carries a horizon in days, a proportional move, a volatility shift, a skew shift, a path model, and a probability.

That output is normalised before anything downstream sees it: probabilities are clamped to a valid range and rescaled to sum to one, and implausible horizons are bounded. If the model call fails or returns nothing usable, a deterministic parser derives the branches from the prompt instead, so an analysis never depends on a model responding. From this point forward there is no language model in the pipeline.

The engine fits a power-law SSVI volatility surface to the current option chain and records its fit error in both total variance and implied-volatility terms, along with basic arbitrage checks. It then calibrates four structural models to the same quotes:

• Bates — stochastic volatility with lognormal jumps.
• Heston — stochastic volatility.
• Merton jump-diffusion — constant volatility with jumps.
• Variance Gamma — a pure-jump process.

Each model's calibration RMSE is retained. Only models whose error is within 4× the best fit are eligible to price anything; the rest are dropped rather than blended in, so a badly-fitting model cannot quietly drag a consensus price. Where a model is unavailable for a cell, the engine falls back in a fixed order — Bates, then Heston, then Black-Scholes, then the SSVI surface, then intrinsic or mid for expiry and path edge cases — and records which pricer actually produced the number.

Every analysis reports the models it used and their fit errors. A run where nothing calibrates well is visible as such rather than presented with the same confidence as one where everything did.

The engine enumerates candidate structures across 29 strategy families — single legs, verticals, butterflies including broken wings, backspreads and ratio spreads, straddles and strangles, iron condors and iron butterflies, ladders, calendars, and diagonals — filtered to the families that fit the stated objective, and built from strikes and expiries that actually exist on the chain.

Each candidate is then priced leg by leg in every branch, producing a modeled profit and loss per structure per scenario. A single run routinely prices well over a thousand candidates across the full scenario grid. Candidates that violate an explicit constraint — including any required P&L floor at a named scenario — are removed before scoring rather than ranked low.

• Probability-weighted modeled P&L — the sum, over branches, of each branch's probability times the candidate's modeled P&L in that branch. This is expected value under your scenario tree, not under the market's implied distribution and not under any historical one.
• Assignment-risk penalty — a fixed charge applied to structures carrying early-assignment exposure from short legs. It is a deliberate, blunt preference against assignment risk, not a modeled cost of it, and it is reported separately so you can see its effect and disagree.
• Model-disagreement penalty — the probability-weighted spread across the surviving calibrated models for that candidate's legs. When the models agree, this is near zero; when they disagree about what a leg is worth, the candidate is charged for the uncertainty instead of being credited with the most flattering price.

Alongside the score, each candidate reports probability of profit, probability of loss, expected shortfall in the losing branches, capital at risk, modeled return on that capital, and the P&L in every individual scenario. Both penalty terms are reported too, so the score is reproducible from the payload rather than something you have to take on faith.

• "Best" means highest-ranked under the scenarios and constraints shown. It is not a claim that a structure is objectively superior. Change a probability or a horizon and the order changes.
• The probabilities are yours, not the market's. They come from your thesis by way of the language model. They are not implied probabilities and they are not estimates of what will happen.
• Modeled P&L is not achievable P&L. It is computed from mid prices and calibrated model values. Real execution involves the bid-ask spread, commissions, slippage, liquidity, and the possibility of not getting filled at all.
• A model that fits today's chain can still be wrong about tomorrow. Calibration measures agreement with current quotes, not predictive accuracy.
• Precise math on a wrong forecast is still wrong. The engine will calculate a bad thesis to several decimal places.