Super Bowl LX

Overview

Price discovery analysis measures which exchange—Kalshi or Polymarket—incorporates new information into prices first. Raw orderbook snapshots from both platforms are aligned at 1-second resolution and analyzed using rolling-window cross-correlation techniques.

Cumulative Price Leadership

At each second, mid-price deltas are computed for both exchanges. A rolling 10-minute window of Pearson cross-correlation across lags −10s to +10s identifies the lag with peak correlation. The exchange whose price moves precede the other's gets credit for that window:

• Positive peak lag: Kalshi moved first (Kalshi's past deltas predict Polymarket's future deltas).
• Negative peak lag: Polymarket moved first.

Leadership counts accumulate over time, so the gap between the two lines shows which exchange has led price formation more often.

Directional Lead-Lag Correlation

Shows the rolling correlation between one exchange's past price changes and the other's future changes:

Kalshi → Poly = corr(deltaK[t−1], deltaP[t])

When “Kalshi → Poly” is higher, Kalshi's moves are more predictive of Polymarket's next move, and vice versa. Both are computed over a rolling 10-minute window.

Cross-Correlation by Lag Offset

Shows Pearson correlation at specific time offsets between the two exchanges' price deltas over a 10-minute rolling window:

• Positive lags (+1s, +3s): Kalshi leads—Kalshi's moves at time t correlate with Polymarket's moves at t+N.
• Negative lags (−1s, −3s): Polymarket leads.
• Lag 0: Simultaneous co-movement.

The lag band with the highest correlation at any given time indicates which exchange is driving price formation and how quickly the other follows.

Cross-Exchange Divergence

The cross-exchange spread (Kalshi mid − Polymarket mid) is smoothed with a 5-minute simple moving average. Persistent non-zero values indicate sustained disagreement between exchanges, which may represent arbitrage opportunities or structural differences in participant composition.

Assumptions & Limitations

• Mid-prices are computed as (best bid + best ask) / 2. If one side is missing, the available side is used.
• Snapshot timestamps are aligned to 1-second buckets. Sub-second ordering within a bucket is not captured.
• Cross-correlation measures linear relationships between price changes. Non-linear lead-lag dynamics are not captured.
• Kalshi prices are in cents (0–100); Polymarket prices are in dollars (0–1). Both are used as-is for correlation, which is scale-invariant.