> ## Documentation Index
> Fetch the complete documentation index at: https://mathematicalcompany.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Horizon Kalshi Market Maker

> Black-Scholes binary pricing on a short-dated Kalshi contract.

A market maker on Kalshi using Black-Scholes binary pricing on a short-dated BTC contract.

## Full Code

```python theme={null}
"""Market maker on Kalshi (paper mode)."""

import math
import horizon as hz
from horizon.context import FeedData


def fair_value(ctx: hz.Context) -> float:
    btc_price = ctx.feeds.get("btc", FeedData()).price or 100_000
    strike = 100_000
    vol = 0.6
    tte = 1 / 365  # 1 day to expiry
    if tte <= 0:
        return 1.0 if btc_price >= strike else 0.0
    d2 = (math.log(btc_price / strike) - 0.5 * vol**2 * tte) / (vol * math.sqrt(tte))
    return 0.5 * (1 + math.erf(d2 / math.sqrt(2)))


def quoter(ctx: hz.Context, fair: float) -> list[hz.Quote]:
    spread = 0.04
    return hz.quotes(fair, spread, size=10)


if __name__ == "__main__":
    hz.run(
        name="kalshi_mm",
        exchange=hz.Kalshi(api_key="demo_key"),
        markets=["KXBTC-25FEB16"],
        feeds={"btc": hz.BinanceWS("btcusdt")},
        pipeline=[fair_value, quoter],
        risk=hz.Risk(max_position=50),
        interval=1.0,
        mode="paper",
    )
```

## How It Works

1. **Fair value** uses the Black-Scholes binary formula with:

* Strike: \$100,000
* Volatility: 60% annualized
* Time to expiry: 1 day (short-dated)
* Underlying: BTC price from Binance WebSocket feed

2. **Quoter** places a fixed 4-cent spread around the fair value with size 10

3. Risk is capped at 50 contracts per market

## Short-Dated vs Long-Dated

For a 1-day contract, the binary option is highly sensitive to the underlying price:

* BTC at $99,000 → fair value ≈ 0.25 (unlikely to hit $100k in 1 day)
* BTC at \$100,000 → fair value ≈ 0.50 (coin flip)
* BTC at \$101,000 → fair value ≈ 0.75 (likely already above)

For longer-dated contracts, increase `tte`:

```python theme={null}
tte = 30 / 365  # 30 days → more moderate pricing
```

## Run It

```bash theme={null}
# Paper mode
python examples/kalshi_mm.py

# Live on Kalshi demo
python -m horizon run examples/kalshi_mm.py --mode=live
```

<Tip>
  Use Kalshi's demo environment for testing: set `api_url="https://demo-api.kalshi.co/trade-api/v2"` or `KALSHI_API_URL` env var.
</Tip>