# Options-Implied Odds (`options_probability`) > Risk-neutral expiry probabilities above or below a price or inside a range, plus implied 68% and 90% ranges. Derived from options forwards and volatility, with smile adjustment where quoted — not calibrated real-world forecasts. - Category: Options - MCP tool: `options_probability` - REST: `GET /options/probability/{currency}` - x402 price: $0.01 per call (USDC on Base) - HTML: https://www.f1ow.com/docs/tools/options_probability ## What it does Risk-neutral probabilities implied by crypto options at one expiry: chance of settling above/below a price or inside a range, expected 68%/90% ranges, lognormal at that expiry's ATM IV and forward plus a smile-adjusted value within quoted strikes. Market-implied odds, not calibrated forecasts. ## Parameters | Name | Type | In | Required | Description | | --- | --- | --- | --- | --- | | `currency` | string | path | yes | Underlying symbol, e.g. "BTC". | | `expiry` | string | query | no | "next" (first expiry ≥ 1 day, default), "2026-12-25" or "25DEC26". | | `price` | number | query | no | Price to get P(above)/P(below) for. | | `range_low` | number | query | no | Range lower bound. | | `range_high` | number | query | no | Range upper bound. | ## Call it ### cURL ```bash curl "https://mcp.f1ow.com/v1/options/probability/BTC?expiry=next&range_low=65000&range_high=80000" \ -H "Authorization: Bearer $F1OW_API_KEY" ``` ### MCP ```json { "jsonrpc": "2.0", "id": 1, "method": "tools/call", "params": { "name": "options_probability", "arguments": { "currency": "BTC", "expiry": "next", "range_low": 65000, "range_high": 80000 } } } ``` ### TypeScript ```ts const res = await fetch("https://mcp.f1ow.com/v1/options/probability/BTC?expiry=next&range_low=65000&range_high=80000", { headers: { Authorization: `Bearer ${process.env.F1OW_API_KEY}` }, }); const data = await res.json(); // the tool's result as JSON, typed in the OpenAPI spec console.log(data); ``` ### Python ```python import os, requests res = requests.get( "https://mcp.f1ow.com/v1/options/probability/BTC?expiry=next&range_low=65000&range_high=80000", headers={"Authorization": f"Bearer {os.environ['F1OW_API_KEY']}"}, ) data = res.json() # the tool's result as JSON, typed in the OpenAPI spec print(data) ``` ### WebSocket ```jsonc // wss://mcp.f1ow.com/v1/ws — subprotocol "jsonrpc-2.0", Authorization: Bearer { "jsonrpc": "2.0", "id": 1, "method": "tools/call", "params": { "name": "options_probability", "arguments": { "currency": "BTC", "expiry": "next", "range_low": 65000, "range_high": 80000 } } } // Or push a fresh result whenever it changes (minimum interval 15 s) { "jsonrpc": "2.0", "id": 2, "method": "subscriptions/subscribe", "params": { "name": "options_probability", "arguments": { "currency": "BTC", "expiry": "next", "range_low": 65000, "range_high": 80000 }, "intervalSeconds": 60 } } ``` ### x402 ```bash # No account: the first call answers 402 with a PAYMENT-REQUIRED challenge; # an x402 client pays it in USDC on Base and retries. curl "https://mcp.f1ow.com/x402/v1/options/probability/BTC?expiry=next&range_low=65000&range_high=80000" ``` ## Sample response Captured 2026-11-13. The JSON is what REST and WebSocket return and the `structuredContent` of an MCP call (trimmed): ```json { "atmIvPct": 47.57, "between": { "high": 80000, "lognormal": 0.985, "low": 65000, "smileAdjusted": 0.962 }, "days": 1, "expiry": "2026-11-14T08:00:00Z", "forwardUsd": 68603.35, "meta": { "ageSeconds": 2, "observedAt": "2026-11-13T08:05:40Z", "provider": "Deribit", "underlying": "BTC" }, "model": "risk-neutral lognormal at expiry ATM IV and forward; smile-adjusted digital within quoted strikes", "prices": [], "quantiles": [ { "cumulative": 0.05, "price": 65835.67 }, { "cumulative": 0.16, "price": 66908.28 }, { "cumulative": 0.5, "price": 68582.18 }, { "cumulative": 0.84, "price": 70297.95 }, { "cumulative": 0.95, "price": 71443.25 } ], "quotedStrikeRange": { "high": 83000, "low": 63000 }, "generatedAt": "2026-11-13T08:05:40Z" } ``` Over MCP the text report a model reads comes with it: ```text === BTC options expiry probabilities — Deribit === Observed 2026-11-13T08:05:40Z (2s ago) | spot index $68615.64 Expiry 14 Nov 2026 08:00 UTC (1.0d) | forward $68603.35 (Deribit, reported) | ATM IV 47.6% of that expiry (calculated; not DVOL) Model: lognormal P(S_T > K) = N(d2) at the forward and ATM IV; smile-adjusted = N(d2(σ(K))) − vega·dσ/dK (Breeden–Litzenberger digital) within quoted strikes $63000.00–$83000.00. Expected range at expiry (lognormal): 68% $66908.28 – $70297.95 | 90% $65835.67 – $71443.25 | median $68582.18 between $65000.00 and $80000.00: 98% (lognormal) | 96% smile-adjusted Risk-neutral odds priced into options (they include risk premia), not real-world or calibrated forecasts; P(touch before expiry) is higher than P(finish beyond). ``` ## Related tools - [Options Chain](https://www.f1ow.com/docs/tools/options_chain) — Calls and puts by strike and expiry: quotes, mark implied volatility, open interest and volume. Reported data is separated from calculated metrics, with coverage and thin-market caveats. - [Implied Volatility](https://www.f1ow.com/docs/tools/options_volatility) — ATM volatility, term structure, implied move size, 25-delta skew and IV versus realized volatility. BTC/ETH volatility-index history adds context. What options price for the size of a move — not its direction. - [Options Positioning](https://www.f1ow.com/docs/tools/options_positioning) — Put/call open interest, strike and expiry concentrations, expiring notional, theoretical max pain and recent option trades. One venue; aggregate open interest does not reveal who is long or short, and max pain is not a forecast. - [Gamma & Hedge Scenarios](https://www.f1ow.com/docs/tools/options_gamma) — Modeled gamma exposure, walls, flip levels and an options regime, with price, time and volatility what-ifs. Dealer hedge ladders depend on an explicit positioning scenario — theoretical sensitivity, not observed dealer orders.