Methodology

Every research tool ships a number where the honest answer is a distribution: a consensus mean, a price target, a single-scenario DCF. That is the opposite of how a derivatives desk thinks. Riptide flips the unit of research from a point estimate to a probability distribution, frames every view as expected value, and does the one thing fundamental tools don't: it puts the analyst's distribution and the options market's implied distribution on the same axis and quantifies the gap as edge.

The risk-neutral density of the terminal price is the discounted second derivative of the call price with respect to strike:

q(K) = e^(rT) · ∂²C/∂K²

It is model-free: it holds for any underlying process under no-arbitrage with European options. A useful corollary gives the market's odds at every price directly from the call-price slope:

P(S_T > K) = 1 + e^(rT) · ∂C/∂K

Intuition worth saying out loud: a long butterfly pays a narrow band around a strike, so its price is the probability mass there. The discrete density we plot is exactly a butterfly spread:

q(K) ≈ e^(rT) · [C(K−ΔK) − 2·C(K) + C(K+ΔK)] / ΔK²

We do notdifferentiate raw quotes, they're too noisy to survive two derivatives and yield ~50% negative densities. Instead we follow Shimko (1993):

1. For each strike, take the liquid out-of-the-money option (put below the forward, call above) and recompute its implied vol from the mid. IV is identical for a call and put at the same strike under put-call parity, so OTM quotes stitch into one clean smile.
2. Fit a natural cubic spline to IV-vs-strike, evaluated on a fine grid.
3. Reprice a smooth call curve via Black-Scholes using the fitted IVs.
4. Take the discrete butterfly second difference above.
5. Beyond the observed strikes we hold IV flat at the wing value, extending the density with lognormal-style tails, then renormalize so it integrates to ~1. (Figlewski grafts parametric GEV tails for more precision; flat-IV extension is the simpler choice we disclose here.)

A correct density is non-negative, integrates to ~1, and its mean sits on the forward. The terminal surfaces those diagnostics; warnings appear when truncation or smile noise pushes them out of tolerance.

Two methods that reconcile, so the work is checkable:

IV method:        EM = S · IV · √(DTE/365)
Straddle method:  EM ≈ 0.85 × ATM straddle price

They agree via Brenner-Subrahmanyam (each ATM option ≈ 0.4·S·σ·√T, so the straddle ≈ 0.8·S·σ·√T). We quote the 0.85 practitioner multiplier desks actually use, distinct from the theoretical EM ≈ 1.25 × straddle, which answers the inverse question. For a catalyst we isolate the move with the first expiry just after the event and surface the IV-crush estimate: the mechanical 30–50% overnight IV collapse that can sink a correct directional call held in long premium.

We replace "price target = $X" with the expected value under the analyst's density:

EV = ∫ payoff(S_T) · f_subjective(S_T) dS_T

A stock can be a buy even when consensus isthe modal scenario, if dispersion or a low-probability / large-payoff tail dominates. Edge is where the subjective density diverges from the options-implied density for a given outcome; we price each candidate structure's expected payoff under the subjective density (discounted by e^(−rT)) against its market cost. A positive gap is the candidate mispricing.

Read this one

The options-implied density is risk-neutral (Q), not real-world (P). Risk aversion inflates down-state probabilities, so the implied distribution is pessimistically skewed versus true odds. The persistent gap is the volatility/variance risk premium: implied vol exceeds subsequently-realized vol on average.

VRP ≈ implied vol − realized vol   (e.g. ATM IV − 30-day realized)

We display the VRP explicitly, label the axis "market-implied (risk-neutral) probability," and offer a transparent risk-premium adjustment (a constant drift tilt) rather than pretending to do a full, contested Ross recovery. Mislabeling Q as P is the red-flag error naive "implied probability" tools make; we don't.

The bet closes with fractional Kelly:

Discrete:    f* = (b·p − q) / b      (b = payoff odds, p = win prob, q = 1−p)
Continuous:  f* = (μ − r) / σ²

We always present half-Kelly. Full Kelly is optimal only if your probabilities are exactly right, which they never are; halving absorbs estimation error and signals you understand parameter risk. f* < 0 means negative EV, don't bet.

Production LLMs are RLHF-overconfident and do not natively emit calibrated probabilities. So we never surface a bare model probability. The model is handed the options-implied (risk-neutral) probabilities as a base rate and must anchor to them, justify any deviation with specific evidence, and return its own overconfidence caveat. The output feeds the same EV engine as a manual view, it doesn't get a special pass.

We score the analyst's own probabilistic calls with a Brier score (mean squared error of probability vs outcome; 0 is perfect, 0.25 is a coin flip answered "50%") and a reliability diagram (when you say X%, does it happen X% of the time?). This grades decision quality independent of any single outcome, process over outcome.

Option chains, quotes, and history come from a free/best-effort source (yahoo-finance2) with SEC EDGAR for filings and fundamentals. The demo runs on baked, internally-consistent snapshots so it can't break live; flip RIPTIDE_FORCE_LIVE=1 to pull live chains for any ticker, with snapshot fallback on error. Everything is labeled delayed / illustrative. Honesty about data provenance is a feature, not a weakness, it assumes you already have Bloomberg and proprietary analytics; Riptide adds the one reasoning layer those don't surface.

Not investment advice. Illustrative research tooling built as an interview demonstration.