How Our OU Model Predicts Funding Rates

When you open a market on Settled, the initial YES/NO prices aren't set by the first trader. They're set by a mathematical model trained on 6.5 years of funding rate data.

That model is an Ornstein-Uhlenbeck (OU) process, a stochastic differential equation designed for mean-reverting time series. Funding rates are textbook mean-reverting: they spike, then decay back toward equilibrium.

The Math

The OU process models funding rate evolution as:

dr = θ(μ - r)dt + σdW

Where:

• r = current funding rate
• θ = mean-reversion speed (how fast rates snap back)
• μ = long-run equilibrium rate (~0.01% for most pairs)
• σ = volatility (how much rates swing between settlements)
• dW = Brownian motion (random noise)

We calibrate θ, μ, and σ for each of the 1,910 symbols in our database using OLS regression on historical settlement sequences.

Calibration Results

The R² of 0.63 means the current rate explains 63% of the variance in the next settlement. That's remarkable for a financial time series.

See the live BTC/USDT funding rate history on Binance or SOL/USDT on Bybit to understand what the model is working with.

From Model to Market Price

When the scheduler creates a market, it queries the OU model for each symbol:

1. Fetch the current live funding rate from the exchange
2. Compute P(positive) using the calibrated parameters
3. Convert probability to LMSR share quantities: q_yes = b × ln(p / (1-p)) / 2
4. This sets the opening YES/NO prices

If the OU model says BTC has a 73% chance of positive funding at next settlement, the market opens at YES 73¢ / NO 27¢.

Directional Accuracy

Across all 1,910 symbols:

• 89% directional accuracy on the top 50 by R²
• High-confidence filter (OU prediction > 70%): 2x the per-settlement expected value
• Selective entry (only 53% of settlements): captures the fat part of the distribution

The model doesn't predict the exact rate. It predicts the sign, positive or negative. For binary markets, that's all you need.

The Edge

The OU model gives Settled's LMSR a built-in house edge. When the initial price is well-calibrated:

• Traders who agree with the model buy at fair value
• Traders who disagree are statistically more likely to lose
• The LMSR collects the spread

At 89% accuracy, the expected LP profit is +$21 per market. At 70%, it breaks even. Below 50%, the vault bleeds. The accuracy dashboard monitors this in real-time with a circuit breaker at 75%.

The model is recalibrated daily from the latest settlement data. Market regimes shift. The model adapts.

---

Related reading:

• Funding Rates Are Prediction Markets — the thesis behind Settled
• Why LMSR Is the Right AMM — how the OU model feeds into market pricing
• Why We Built Settled — the origin story
• Browse Live Markets — see OU-priced markets in action
• Binance BTC/USDT Funding Rate — the primary symbol the OU model is calibrated on