Bachelier
Bachelier is a peer-to-pool covered-call options vault on sBTC, on Stacks — with options priced on-chain by a fixed-point Black–Scholes engine written in Clarity.
Depositors add sBTC and receive bcSHARE pro-rata. Each weekly round the keeper opens a slightly out-of-the-money (OTM) strike from the BTC-USD oracle; takers buy 1-sBTC call contracts and pay USDC premium that accrues to depositors immediately via a premium-per-share index. At expiry the round settles against the oracle.
Named after Louis Bachelier, whose 1900 thesis Théorie de la spéculation first applied a random-walk model to option pricing — five years before Einstein, and seventy before Black–Scholes.
Settlement in one screen
At expiry, with spot S_exp and strike K:
S_exp ≤ K— calls expire worthless. The pool keeps all sBTC and all premium.S_exp > K— each contract owes(S_exp − K) / S_expsBTC (always less than 1), paid out of collateral via pull-basedexercise; the rest returns to the pool.
The pool can never write more contracts than the whole sBTC it holds, so it is always fully collateralized — settlement needs no external liquidity, and premium only ever flows in.
Reference economics
Asserted in tests at every layer (Clarity, the TS mirror, and the API):
| Input | Value |
|---|---|
| Spot | ≈ $104,210 |
| Strike | +10% OTM |
| Implied volatility | 0.55 |
| Tenor | 1 week |
| Risk-free rate | 0.04 |
| Premium / contract | ≈ $430 (bs-call-price reference vector = 42848661381) |
| Yield | ≈ 0.41%/week ≈ 23–24% APY |
Trust model
The browser signs all user-fund transactions via the wallet (Leather /
Xverse). The only server-side signer is the keeper, and it can only drive
the round lifecycle (start-round / settle-round) — it can never touch user
funds. The REST API is read-only; no service ever holds a user key.
Live on testnet
A full deployment is live on Stacks testnet:
- Deployer / keeper-owner:
ST1QN0P1MB429DHV28KT68F80621FHE4NE880CBZK - Web app: bachelier-frontend.vercel.app
- 60 demo users have funded, minted, and deposited — see Test Users.
Continue to the Architecture overview, or jump straight to Vault mechanics.