PredictionX
Pricing Engine & Strategy Agent

§ 01Overview

PredictionX prices binary prediction market contracts on Kalshi. A Kalshi commodity contract is economically equivalent to a cash-or-nothing digital option: it pays $1 if a commodity price exceeds (or falls below) a strike level $K$ on a given settlement date, and $0 otherwise.

The engine computes a fair probability $\hat{p}$ for each contract through a four-stage pipeline:

The edge is then $\text{edge} = \hat{p} - p_{\text{market}}$, where $p_{\text{market}}$ is the independently quoted Kalshi mid-price for the relevant side.

§ 02Kalshi Binary Contracts

A Kalshi commodity contract resolves to YES ($1) or NO ($0) at expiry based on a single condition:

where $S_T$ is the underlying commodity spot price at settlement date $T$, and $K$ is the strike price parsed from the ticker suffix (e.g. -T80 → $K = \$80$).

The risk-neutral fair value equals the risk-neutral probability:

YES and NO prices are independently quoted

Kalshi operates a separate orderbook for each side. YES and NO bid/ask are quoted independently by market makers:

Example on a liquid contract:

The 2¢ gap is the market-maker's spread collected when YES and NO are sold simultaneously. Buying YES at ask (44¢) and NO at ask (61¢) costs 105¢ > $1 — no arbitrage.

Edge against the correct side's price

Because $p_{\text{YES,mkt}} + p_{\text{NO,mkt}} \neq 1$, YES and NO edges are not equal-and-opposite. A wide-spread contract can show positive edge on both sides simultaneously.

§ 03Futures Price Strip

A futures strip is the set of quoted futures prices across all liquid delivery months for a commodity. For WTI crude (root CL):

Ticker construction follows CME naming conventions: root + month code + 2-digit year + exchange suffix.

Exchange suffixes: .NYM (NYMEX energy/metals), .CMX (COMEX precious metals), .CBT (CBOT grains), .CME (CME livestock/indices/crypto).

§ 03bPyth Network Spot Price — Gold & Silver

Two series — KXGOLDD and KXSILVERD — settle on a Pyth Network spot price feed, not on COMEX futures. Kalshi's specifications for these series reference Pyth's 1-minute candle close for XAU/USD and XAG/USD respectively. Using the COMEX futures price as the anchor for these contracts would be systematically wrong.

Settlement Kinds

How the Pyth Anchor Is Applied

For pyth_spot series, the pricing flow calls data/pyth.py to retrieve the current Pyth spot price and then calls apply_spot_anchor(strip, spot_price), which replaces the strip's front-month price with the live Pyth spot and returns the adjusted strip plus computed basis:

Pyth Staleness Guard

Each price returned by get_spot_price() is validated against its publish_time field. A price whose publish timestamp is more than 180 seconds behind wall-clock is rejected with PythAPIError — mirroring the yfinance frozen-data guard in data/futures.py.

§ 04Forward Price Interpolation

The key input to the pricing formula is the forward price $F$ — the expected futures price at the contract's settlement month. If the exact settlement month is in the strip, it is used directly. Otherwise we interpolate in log-price space:

where $t_1 \le T \le t_2$ are the nearest delivery dates bracketing the settlement date, measured in calendar ordinals. Interpolating in log-price rather than price space preserves positivity and is consistent with the log-normal dynamics. When $T$ is beyond the last strip date, the last price is used (flat extrapolation).

§ 05Volatility Estimation

Volatility $\sigma$ is the annualised standard deviation of log-returns. Two estimation regimes apply depending on time-to-expiry:

Long-Term Regime (DTE ≥ 7 Days)

252 calendar days of daily closing prices are fetched for the continuous front-month contract (ticker {root}=F). Log-returns are computed and annualised:

The $\sqrt{252}$ annualisation assumes 252 trading days per year. The engine clips the result to $[0.05,\ 2.00]$ to prevent extreme values from degenerate data.

Short-Term Regime (DTE < 7 Days)

For short-dated contracts, 5 days of hourly price data are used, with an asset-class-specific annualisation factor:

Energy and commodity markets trade nearly around the clock (one maintenance hour excluded). Using asset-class-specific $H_{\text{year}}$ prevents over- or under-stating intraday vol.

§ 06The Log-Normal Price Model

The engine models the terminal price $S_T$ as log-normally distributed under the risk-neutral measure $\mathbb{Q}$:

where:

• $F = F(T)$ is the futures price at the settlement month — the risk-neutral expectation of $S_T$
• $\sigma_T = \sigma \sqrt{T}$ is the total volatility over the remaining time $T$ (in years)
• The $-\tfrac{1}{2}\sigma_T^2$ term is the Itô correction keeping $\mathbb{E}^{\mathbb{Q}}[S_T] = F$

This is the Black (1976) futures pricing model applied to binary options — the industry standard for commodity options and OTC derivatives on futures.

§ 07The d₂ Formula — Core Probability Calculation

Given the log-normal model, the probability that $S_T$ exceeds the strike $K$ has a closed-form solution — the digital option pricing formula, derived by integrating the log-normal density above $K$:

where $N(\cdot)$ is the standard normal CDF $N(x) = \int_{-\infty}^{x} \frac{1}{\sqrt{2\pi}} e^{-t^2/2} \, dt$.

Derivation

We want $\mathbb{Q}(S_T > K)$. Since $\ln S_T \sim \mathcal{N}(\mu_T, \sigma_T^2)$ with $\mu_T = \ln F - \frac{1}{2}\sigma_T^2$:

Let $Z = (\ln S_T - \mu_T)/\sigma_T \sim \mathcal{N}(0,1)$. Then:

Intuitive Interpretation of d₂

Relationship to Black-Scholes d₁ and d₂

In standard Black-Scholes for a vanilla call, $d_1 = d_2 + \sigma_T$. The call price is $C = F \cdot N(d_1) - K \cdot N(d_2)$, where $N(d_2)$ is the probability of exercise and $N(d_1)$ is the delta. For our cash-or-nothing digital, there is no delivery of the underlying — only $N(d_2)$ matters.

Total Volatility $\sigma_T$

Two floors prevent degenerate $\sigma_T = 0$ at expiry: long-term mode floors DTE at 1 day ($\tau_{\min} = 1$); short-term mode floors $h$ at 0.25 hours (15 minutes). One exception: the curve endpoint at $\tau = 0$ is computed before any floor, using the deterministic boundary rule $p(0) = \mathbf{1}_{F > K}$, ensuring DTE=0 shows 100%/0% exactly.

§ 08Time-Value Decay Curve

The distribution fit gives $p_{\text{base}}$ — the probability evaluated at today's DTE. As expiry approaches, the contract's probability drifts toward its final 0 or 1 value. The time-value decay curve models this path.

For each DTE $\tau$ from today down to expiry, the engine applies the same log-normal formula with the remaining time:

At $\tau = 0$, the outcome is deterministic: $p(0) = \mathbf{1}_{F > K}$. The full curve is a list of $(\tau,\ p(\tau))$ pairs.

Shape of the Curve

• Deep ITM ($F \gg K$): $p$ starts high and increases monotonically toward 1.0 — less time for price to fall below $K$.
• Deep OTM ($F \ll K$): $p$ starts low and decreases toward 0.0 — less time for a rally to reach $K$.
• ATM ($F \approx K$): $p \approx 0.5$ throughout with a gentle final convergence.
• Near-strike, high vol: the curve is flatter, with a sharp final convergence as $\sigma_T \to 0$.

§ 09Scenario Analysis (±1σ Shocks)

Three scenario probabilities are computed by shocking the forward price by ±1 standard deviation of the log-return over the remaining life:

Note that $\sigma_T$ in the denominator of $d_2$ is unchanged — we shock the expected price path while keeping residual uncertainty fixed. This gives a spread of outcomes bracketing the base case.

§ 10Aggregation — Final Fair Value

1. $p_{\text{base}}$: log-normal probability from the distribution fit. Anchors the estimate.
2. $p_{\text{tv}}$: the decay-curve value at today's DTE. Mathematically equivalent to $p_{\text{base}}$ under the same time scaling, but the time-value module also produces the full $\{\tau,\ p(\tau)\}$ curve for visualisation and forward simulation.
3. $\hat{p}$: the final engine fair value, equal to $p_{\text{tv}}$. If the time-value module fails, the aggregator falls back to $\hat{p} = p_{\text{base}}$.

Scenarios (bull/base/bear) are computed separately using $\pm 1\sigma_T$ forward shocks — see §9. They are reported alongside $\hat{p}$ but do not participate in its definition.

§ 11Short-Term Mode (DTE < 7 Days)

Contracts expiring within 7 days receive special treatment because:

• Daily closing-price vol is too coarse — a lot can happen in hours
• Integer DTE (0 or 1) provides insufficient precision for time scaling $T$
• Expiry times matter: a contract at 4:00 PM vs 11:59 PM EST is very different at DTE=0

$h$ is computed from the Kalshi API's close_time field (ISO 8601 UTC) minus current UTC time, giving sub-hour precision. The decay curve in short-term mode shows 8 evenly-spaced hourly points from now to expiry.

§ 12Volatility Annualisation — Regime Reference

The 23h/day assumption accounts for the maintenance window in electronic futures markets (typically 1 hour around 5–6 PM ET). Equity index futures use 17h because extended-hours sessions have much lower liquidity.

§ 13Edge Score

The market price $p_{\text{mkt}}$ is always sourced from the Kalshi API mid-price (never entered manually). Interpretation:

§ 14Backtesting and Model Evaluation

Once a contract settles, the engine evaluates the prediction using proper scoring rules — mathematical measures that reward honest probability estimates and cannot be gamed by reporting extreme probabilities.

Brier Score

where $\hat{p}_i \in [0,1]$ is the model's fair value and $o_i \in \{0, 1\}$ is the actual outcome. Reference values:

• BS = 0.00: perfect predictions
• BS = 0.25: equivalent to guessing 50% on every contract
• BS = 1.00: perfectly wrong on every prediction

Brier Skill Score (BSS)

BSS > 0 means the model beats the market price as a probability estimator. BSS is the primary long-run measure of whether the engine adds value beyond using the market mid as your forecast.

Calibration

A model is well-calibrated if, across all contracts where it predicted probability $p$, the event actually occurred $p$ fraction of the time. The engine bins predictions into 10pp buckets:

Mean Absolute Error and Bias

Positive bias means the model systematically overestimates the probability of the event occurring.

Edge Direction Accuracy

PnL per Dollar Risked

Averaging this over all runs in an edge bucket gives the realised expected value of acting on that edge signal. Positive average PnL in the high-edge bucket validates the model's alpha.

§ 15Agent Pipeline Overview

The autonomous strategy agent runs a continuous scan-price-signal-size-record loop, evaluating all open Kalshi contracts and recording sizing decisions in shadow mode by default. Every decision is persisted to the strategy_decisions table with full provenance so the loop can be evaluated like a live trading system.

§ 16Pre-Signal Filters

Six filters are applied before any pricing or database lookup — ordered cheapest to most expensive. The first failing check short-circuits evaluation.

TTX Regime Split

A contract is classified as short-term if dte_hours ≤ 26 (approximately one trading day). Short-term contracts use hourly volatility and TTX buckets. Medium-term contracts use daily DTE and daily vol. The agent applies separate TTX/DTE range filters for each regime.

§ 17Confidence Regression and Adjusted Edge

A raw-edge threshold alone ignores whether the pricing model's edge estimates are systematically over- or under-stated in specific market segments. The agent estimates a linear regression from historical raw_edge to realised PnL per dollar risked, fitting two coefficients that capture bias and calibration quality independently.

Training Data

OLS Regression

Interpreting the coefficients:

• $\alpha$ (intercept — bias): expected PnL when raw_edge = 0. If $\alpha < 0$, the model loses on zero-edge trades — systematic overconfidence or adverse selection.
• $\beta$ (slope — calibration): additional realised PnL per unit of raw_edge. $\beta = 1$ means raw edge is perfectly predictive; $\beta < 1$ means edges are overstated; $\beta > 1$ means the model is conservative.

Adjusted Edge Formula

Fallback Prior

When fewer than min_samples (default 50) resolved runs exist for a segment, the agent falls back to a conservative neutral prior:

Confidence Hierarchy

TTX buckets for short-term: <2h, 2–4h, 4–8h, 8–16h, 16–26h. DTE buckets for medium-term: 1d, 2–3d, 4–7d, 8–14d.

§ 18Signal Classification

Two thresholds govern classification:

• $\theta$ — the segment-overridden minimum adjusted edge. Starts at min_adjusted_edge (default 0.072) and may be raised/lowered by a min_edge_override. Used for the watch/buy boundary.
• $\theta_0$ — the global, unoverridden config.min_adjusted_edge (default 0.072). Used exclusively for the auto-buy/clear-buy boundary at $2\theta_0$. Segment overrides never move this line.

LLM Observability (Startup Preflight)

§ 19Position Sizing

Kelly Criterion for Binary Contracts

A Kalshi YES contract bought at price $p_{\text{mkt}}$ has payoff structure: win (probability $\hat{p}$) profit = $1 - p_{\text{mkt}}$; lose (probability $1 - \hat{p}$) loss = $p_{\text{mkt}}$. The Kelly fraction maximises expected log-wealth growth. For net odds $b = (1 - p_{\text{mkt}}) / p_{\text{mkt}}$:

A half-Kelly multiplier $\lambda = 0.5$ and a hard cap $f_{\text{max}}$ (default 10% of bankroll) reduce variance and ruin risk:

Cash-on-Hand Sizing and EV-Ranked Allocation

Within a single cycle, candidates are funded in decreasing order of $f^*$. After each buy, $W_{\text{avail}}$ is decremented before the next candidate is sized:

Fixed Strategy

where $A$ is a constant dollar amount (default $50) and $\theta$ is the same segment-overridden threshold used for Kelly classification. Fixed is a benchmark: lower variance than Kelly but does not scale with edge conviction.

Bankroll Tracking

This is the dollar profit from buying size_USD worth of contracts at $p_{\text{mkt}}$: each dollar spent buys $1/p_{\text{mkt}}$ contracts, each paying $1 or $0 at settlement. Snapshots are append-only and never amended.

§ 20Segment Overrides and Periodic Review

The agent runs a periodic review at most daily, or when review_sample_threshold (default 50) new resolutions have accumulated since the last review. The review identifies market segments where the confidence regression is systematically wrong and applies segment overrides that take effect immediately — no restart required.

Review Process

1. Load analytics views (v_by_ttx_bucket, v_by_dte_bucket, v_by_moneyness, v_strategy_comparison, etc.)
2. Flag segments with n ≥ review_min_segment_n (default 30) and edge accuracy below 0.45 or above 0.65.
3. Call claude-sonnet-4-6 with tool use — the LLM can query allowed analytics views, inspect bankroll curves, and retrieve prior overrides.
4. LLM returns override recommendations as structured JSON.
5. Overrides are written to segment_overrides and take effect on the next agent cycle.

Override Types

§ 21Live-Mode Safety Guards

The live execution path applies a layered set of safety checks introduced after Day-1 of live trading exposed several failure modes. All guards are evaluated in order; the first failing guard determines the skip reason.

Data-Quality Guards (Before Pricing)

Per-Order Live Guards (Before Placing a Kalshi Order)

These guards evaluate against a per-cycle running state (_LiveCycleState) so two candidates within the same cycle cannot collectively breach a cap that each one would pass individually.

§ 22Model Limitations and Assumptions

Log-Normal Dynamics

The model assumes continuous log-normal price paths. Real commodity prices exhibit:

• Jump risk: sudden gap moves from OPEC announcements, weather events, geopolitical shocks
• Fat tails: extreme moves occur more frequently than the normal distribution predicts
• Mean reversion: energy prices tend to revert to long-run equilibrium cost of production

Constant Forward Price

The forward price $F$ is interpolated from today's futures strip and held constant throughout the decay curve. In practice, $F$ shifts as new information arrives.

Constant Volatility

A single annualised $\sigma$ is used throughout the remaining contract life. Real markets exhibit a volatility term structure and a volatility smile. The engine uses a single number — adequate for ballpark fair-value estimation, not for precision near-the-money pricing.

Risk-Neutral vs. Real-World Measure

The engine operates under $\mathbb{Q}$, using the futures price as the expected terminal value. Risk premiums (e.g., the crude oil risk premium embedded in backwardation) are implicitly absorbed into the futures price but not separately modelled.

Short-Term Forward Price Accuracy

For very short-dated contracts, the front-month futures price is a reasonable proxy for the eventual settlement price, but intraday basis can be significant. A more precise implementation would use the specific expiry-month contract's last traded price.

§ 23Glossary