kalshi-crypto-index-markets Checked

Φ is the standard normal CDF. Unlike temperature brackets (which settle on integers), price brackets settle on a continuous reference price — the half-integer continuity correction used for weather is **not applicable here**. Do not add ±0.5.

### Sourcing σ

• **Realized vol:** rolling 5- or 20-day realized volatility of the underlying, scaled to the settlement horizon.
• **Implied vol:** the ATM IV from listed options (SPX/NDX for index, CME/Deribit for crypto) is a forward-looking σ that already embeds the market's distributional view for the horizon.
• **Hourly markets:** for BTC/ETH hourlies, σ is the 1-hour IV or intraday realized vol. Σ shrinks rapidly — even small absolute moves land in a different bracket. Sensitivity is high; prefer IV-derived σ.

For daily markets, a simple log-return diffusion gives σ_daily ≈ σ_annual / √252 for index, or the equivalent annualized vol / √365 for crypto. Express in price units (not %) before inserting into the formula.

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Decision Timing — Close-Offset, Not a City Hour

**This is the key difference from weather markets.**

Weather settles on a daily extreme that occurs at some unknown intraday time. The decision book is read near the likely peak/trough (a city-local hour).

Crypto and index markets settle at a **fixed reference close**:

• Daily S&P 500 / Nasdaq-100: the official market close (4:00 PM ET).
• Daily BTC/ETH: a defined reference close published in the market's rulebook.
• Hourly BTC/ETH: the close of each hour interval per the rulebook.

The practical convention used in production:

DECISION_OFFSET_MINUTES = 120   # read book ~2h before settlement close
decision_ts = settlement_close_ts - timedelta(minutes=DECISION_OFFSET_MINUTES)

This offset balances information freshness (IV and order-book signal) against the risk of being front-run by news that drops in the final window. Tune per-series based on your fill-rate observations.

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Settlement — Verify the Rulebook Reference

Settlement is on Kalshi's own result field. **Do not re-derive from an external feed.** The exact reference price for each series (e.g., official SPX close vs. a crypto composite) is specified per-market in the Kalshi rulebook.

Honest caveat: the exact reference price spec was not pinned for every series during development. Before trading any new series, read the market's rulebook and confirm:

1. The settlement price source (exchange, composite, or Kalshi-computed).

2. The settlement time and timezone.

3. Whether the bracket is inclusive/exclusive at the boundary.

Backtesting against a price feed that differs from the true settlement source is the primary way to manufacture fake edge in these markets.

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Edge: Longshot-Sell Generalization

The **favorite–longshot bias** generalizes from weather to index and crypto brackets. Tail brackets are systematically overpriced relative to a Gaussian model calibrated to realized/implied vol; interior brackets near the current underlying level are fairly priced or underpriced.

### Evidence (be precise about depth)

From production testing with a rotating CV approach, Kalshi-settled outcomes, fee-inclusive:

| Market type | Sweet band | Edge direction | Sample | Result |

|-------------|-----------|----------------|--------|--------|

| **Index** | Market-implied P ∈ [0.05, 0.20] | Longshot-sell (short tail brackets) | ~50 trades | ~+1.7% taker / ~+9% maker |

| **Crypto daily** | — | — | Too sparse | Inconclusive |

| **Crypto hourly** | — | — | Too sparse | Inconclusive |

**Interpret conservatively.** ~50 trades is not a stable estimate; confidence intervals are wide. The index result is directionally consistent with the weather finding and prior literature on longshot bias, but treat it as a hypothesis to validate forward, not a confirmed edge.

### The HFT Caveat (critical for hourlies)

Crypto and index markets settle on public, real-time price ticks. The underlying is continuously quoted on liquid venues with sub-millisecond latency. This means:

• The information content of any bracket price is rapidly arbitraged by HFT and market-maker algos watching the same tick.
• **Latency front-running** — buying or selling brackets based on price moves — is a colocation/HFT game. From a retail connection you will be consistently on the wrong side of news-driven bracket repricing.
• The retail-feasible angle is the **structural longshot-sell** (exploiting the persistent overpricing in cheap tails that is stable across market regimes), not speed-based positioning.
• Hourly crypto markets are the most HFT-contested of all Kalshi markets. Maker fills on tail brackets may be scarce precisely when the edge is largest.

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Market Microstructure Notes

• **Overround** is the primary microstructure signal. For a partition of N brackets, overround = Σ P_yes. When overround > 1.10 in the tails, the aggregate tail sell has positive expected value before fees; after Kalshi taker fees (~7 cents/$1 per leg) the bar is higher. Maker rebates change the math substantially.
• **Thin books:** individual bracket markets on hourly crypto may show wide spreads and low depth. Model a realistic fill at a depth level before sizing.
• **Basket dutch:** selling the complete set of tail brackets is not trivially an arb even when overround > 1.0; fees per leg plus execution uncertainty can eliminate the overround advantage. See `pre