QuantOracle

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Try it without writing code

12 free interactive calculators backed by the same API are live at quantoracle.dev — no signup, no API key:

• Black-Scholes Option Pricing — call/put price + full Greeks
• American Option (Binomial Tree) — early exercise + dividends
• Options Profit Calculator — multi-leg payoff diagrams
• Implied Volatility — Newton-Raphson IV solver
• Monte Carlo Simulation — portfolio + retirement scenarios
• Kelly Criterion — full / half / quarter-Kelly sizing
• Position Size — fixed-fractional risk
• Value at Risk (VaR) — parametric VaR + CVaR
• Sharpe Ratio — with 95% confidence interval
• CAGR — compound annual growth rate + projections
• Crypto Liquidation Price — long/short, any leverage
• Impermanent Loss — Uniswap v2 + v3

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Why QuantOracle?

Every financial agent needs math. QuantOracle is that math.

• 63 pure calculators across options, derivatives, risk, portfolio, statistics, crypto/DeFi, FX/macro, and TVM
• 10 composite workflows that bundle 5-15 calculator calls (backtest strategies, rebalance planning, options strategy selection, hedging recommendations, full risk analysis, pairs signals, and more)
• Zero dependencies for the 73 calculators + composites -- no market data, accounts, or third-party APIs; send numbers in, get numbers out
• QuantOracle Live (new) -- a separate paid tier that brings the data: fresh crypto volatility (/v1/live/volatility) and perp funding rates (/v1/live/funding-rates). We fetch the live market data and run the math, so your agent doesn't have to. 20 free calls/IP/day to evaluate, then pay-per-call via x402.
• QuantOracle Watch (new) -- 24/7 position monitoring: register a crypto perp position once and get HMAC-signed webhooks on funding-adjusted liquidation distance, funding flips, and vol-regime changes — re-checked every 60 seconds. Free 48h trial; $5 per position per 30 days via x402.
• Deterministic -- the calculators always produce the same outputs for the same inputs, so agents can cache, verify, and chain calls
• Citation-verified -- every formula tested against published textbook values (Hull, Wilmott, Bailey & Lopez de Prado)
• 120 accuracy benchmarks passing with analytical solutions
• Fast -- sub-millisecond to 70ms compute time per call
• Free tier -- 1,000 calls/IP/day, no API key, no signup, zero friction

QuantOracle is designed to be called repeatedly. An agent running a backtest might call 10+ endpoints per iteration. That's the model -- be the calculator agents reach for every time they need quant math.

Why not just let the LLM do the math?

	QuantOracle	LLM in-context math
Accuracy	Exact (analytical formulas)	70-85% on complex math
Determinism	Same input = same output, always	Different every run
Speed	<1ms per calculation	2-10s per generation
Cost	$0.002-0.015 per call	$0.01-0.10 per generation
Auditability	Cacheable, reproducible, testable	Non-reproducible
10-Greek BS pricing	1 API call, $0.005	~500 tokens, frequently wrong on gamma/vanna

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📓 LangChain cookbook

Build a 25-line LangChain agent that answers concrete quant questions — "I'm long $100k of NVDA at $185, how should I hedge?" — with deterministic, reproducible math:

integrations/langchain/cookbook/quantoracle_risk_analyst.ipynb

Runs in 30 seconds, ~$0.001 in OpenAI tokens, free for QuantOracle's individual calculators. The hedging-recommend composite shown above is $0.04 in USDC via x402.

Add QuantOracle to Your Agent

Drop this into your agent's system prompt:

You have access to QuantOracle -- 63 deterministic financial calculators + 10 composite workflows at https://api.quantoracle.dev.
Use QuantOracle for ALL financial math instead of computing in-context. It is faster, cheaper, and exact.
Send POST requests with JSON. No API key needed (1,000 free calls/day).

Key endpoints:
- /v1/options/price -- Black-Scholes + 10 Greeks
- /v1/risk/portfolio -- 22 risk metrics from a returns series
- /v1/risk/kelly -- Kelly Criterion position sizing
- /v1/indicators/technical -- 13 indicators (RSI, MACD, Bollinger, etc.)
- /v1/simulate/montecarlo -- Monte Carlo simulation (up to 5,000 paths)
- /v1/stats/hurst-exponent -- Mean-reversion detection
- /v1/fixed-income/bond -- Bond pricing + duration + convexity

Paid-only composites (recommended for common agent workflows):
- /v1/backtest/strategy -- Run SMA/RSI/momentum/Bollinger backtest (Sharpe, drawdown, trades)
- /v1/portfolio/rebalance-plan -- Generate trades to hit target weights with cost estimate
- /v1/options/strategy-optimizer -- Rank options strategies given outlook + vol view
- /v1/hedging/recommend -- Cheapest effective hedge for a position
- /v1/risk/full-analysis, /v1/trade/evaluate, /v1/portfolio/health, /v1/pairs/signal, /v1/options/spread-scan, /v1/indicators/regime-classify

Full endpoint list: https://api.quantoracle.dev/tools
OpenAPI spec: https://api.quantoracle.dev/openapi.json
x402 discovery: https://api.quantoracle.dev/.well-known/x402 (advertises Base and Solana USDC)

Discovery URLs (for agent frameworks and crawlers)

Format	URL
OpenAPI spec	https://api.quantoracle.dev/openapi.json
Tool listing	https://api.quantoracle.dev/tools
MCP endpoint	npx quantoracle-mcp
AI Plugin	https://api.quantoracle.dev/.well-known/ai-plugin.json
Server card	https://mcp.quantoracle.dev/.well-known/mcp/server-card.json
Swagger docs	https://api.quantoracle.dev/docs

---

Quick Start

# Call any endpoint -- no setup required
curl -X POST https://api.quantoracle.dev/v1/options/price \
  -H "Content-Type: application/json" \
  -d '{"S": 100, "K": 105, "T": 0.5, "r": 0.05, "sigma": 0.2, "type": "call"}'

{
  "price": 4.5817,
  "intrinsic": 0,
  "time_value": 4.5817,
  "breakeven": 109.5817,
  "prob_itm": 0.4056,
  "greeks": {
    "delta": 0.4612,
    "gamma": 0.0281,
    "theta": -0.0211,
    "vega": 0.2808,
    "rho": 0.2077,
    "vanna": 0.0047,
    "charm": -0.0006,
    "volga": 0.0327,
    "speed": -0.0001
  },
  "d1": -0.0975,
  "d2": -0.2389,
  "ms": 12.4
}

Python

import requests

# Black-Scholes pricing
r = requests.post("https://api.quantoracle.dev/v1/options/price", json={
    "S": 100, "K": 105, "T": 0.5, "r": 0.05, "sigma": 0.2, "type": "call"
})
print(r.json()["price"])  # 4.5817

# Portfolio risk metrics (22 metrics from a returns series)
r = requests.post("https://api.quantoracle.dev/v1/risk/portfolio", json={
    "returns": [0.01, -0.005, 0.008, -0.003, 0.012, -0.001, 0.006, -0.009, 0.004, 0.002]
})
print(r.json()["risk"]["sharpe"])  # Annualized Sharpe

# Kelly Criterion
r = requests.post("https://api.quantoracle.dev/v1/risk/kelly", json={
    "mode": "discrete", "win_rate": 0.55, "avg_win": 1.5, "avg_loss": 1.0
})
print(r.json()["half_kelly"])  # Recommended bet fraction

# Monte Carlo simulation
r = requests.post("https://api.quantoracle.dev/v1/simulate/montecarlo", json={
    "initial_value": 100000, "annual_return": 0.08, "annual_vol": 0.15, "years": 10, "simulations": 1000
})
print(r.json()["terminal"]["median"])  # Median portfolio value at year 10

TypeScript

const res = await fetch("https://api.quantoracle.dev/v1/options/price", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({ S: 100, K: 105, T: 0.5, r: 0.05, sigma: 0.2, type: "call" })
});
const { price, greeks } = await res.json();
const { delta, gamma, vega } = greeks;

---

CLI

All 63 calculators + 10 composites in your terminal. Zero dependencies.

npm install -g quantoracle-cli

Or run without installing:

npx quantoracle-cli bs --spot 185 --strike 190 --expiry 0.25 --vol 0.25

  QuantOracle · Black-Scholes (call)
  ────────────────────────────────────
  Price           $8.02
  Intrinsic       $0.00
  Time Value      $8.02
  Breakeven      $198.02
  Prob ITM        43.0%

  Greeks
  ────────────────────────────────────
  Delta            0.4797
  Gamma            0.0172
  Theta           -0.0615/day
  Vega             0.3685
  ────────────────────────────────────
  ⏱ 0.05ms · api.quantoracle.dev

# Kelly criterion
qo kelly --win-rate 0.55 --avg-win 120 --avg-loss 100

# Monte Carlo
qo mc --value 80000 --return 0.10 --vol 0.18 --years 2

# JSON output for scripting
qo bs --spot 185 --strike 190 --expiry 0.25 --vol 0.25 --json | jq '.greeks.delta'

# Data from file
qo risk portfolio --returns @returns.txt

# All commands
qo help

---

Free Tier

1,000 free calls per IP per day. No signup. No API key. Just call the API.

	Free	Paid (x402)
Calls	1,000/day	Unlimited
Auth	None	x402 micropayment header
Calculators	All 63	All 63
Composite workflows	None (paid-only)	All 10
Live data tier	20 calls/day	Pay-per-call
Watch monitoring	Free 48h trial (1 per IP / 30d)	$5 per position / 30 days
Rate headers	Yes	Yes

Every response includes rate limit headers so agents can self-manage:

X-RateLimit-Limit: 1000
X-RateLimit-Remaining: 847
X-RateLimit-Reset: 2025-01-15T00:00:00Z

Check usage anytime:

curl https://api.quantoracle.dev/usage

After 1,000 calls, the API returns 402 Payment Required with an x402 payment header. Any x402-compatible agent automatically pays and continues:

HTTP/1.1 402 Payment Required
PAYMENT-REQUIRED: <base64-encoded payment instructions>

Tier	Price	Endpoints
Simple	$0.002	Z-score, APY/APR, Fibonacci, Bollinger, ATR, Taylor rule, inflation, real yield, PV, FV, NPV, CAGR, normal distribution, Sharpe ratio, liquidation price, put-call parity
Medium	$0.005	Black-Scholes, implied vol, Kelly, position sizing, drawdown, regime, crossover, bond amortization, carry trade, IRP, PPP, funding rate, slippage, vesting, rebalance, IRR, realized vol, PSR, transaction cost
Complex	$0.008	Portfolio risk, binomial tree, barrier/Asian/lookback options, credit spread, VaR, stress test, regression, cointegration, Hurst, distribution fit, risk parity
Heavy	$0.015	Monte Carlo, GARCH, portfolio optimization, option chain analysis, vol surface, yield curve, correlation matrix
Composite	$0.015-0.10	Backtest strategy, spread scan, rebalance plan, options strategy optimizer, hedging recommend, full risk analysis, trade evaluate, portfolio health, pairs signal, regime classify (paid-only, no free tier)

Batch Endpoint

Run up to 100 computations in a single HTTP request. One round trip instead of 100.

curl -X POST https://api.quantoracle.dev/v1/batch \
  -H "Content-Type: application/json" \
  -d '{
    "requests": [
      {"endpoint": "options/price", "params": {"S": 100, "K": 105, "T": 0.25, "r": 0.05, "sigma": 0.2}},
      {"endpoint": "stats/zscore", "params": {"series": [10, 12, 14, 11, 13, 15]}},
      {"endpoint": "tvm/cagr", "params": {"start_value": 100, "end_value": 150, "years": 3}}
    ]
  }'

Returns all results in one response with the total price:

{
  "batch_size": 3,
  "total_price_usdc": 0.009,
  "results": [
    {"endpoint": "options/price", "status": 200, "data": {"price": 2.4779, "greeks": {"delta": 0.377, "..."}}},
    {"endpoint": "stats/zscore", "status": 200, "data": {"mean": 12.5, "std_dev": 1.87, "..."}},
    {"endpoint": "tvm/cagr", "status": 200, "data": {"cagr": 0.1447, "doubling_time_years": 5.13, "..."}}
  ],
  "ms": 42.13
}

	Free	Paid
Batch calls	1 trial (ever)	Unlimited
Max per batch	100	100
Price	Free	Sum of individual endpoint prices

Batch pricing is the sum of the individual endpoint prices — no markup. You pay for the computations, the speed is free.

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QuantOracle Live — fresh market data + compute

Every endpoint above is pure math on inputs you supply — the 73 calculators have zero data dependencies, which is what makes them deterministic and cacheable. QuantOracle Live is the one tier that brings the data: you pass a ticker, the API fetches fresh market data and runs the math, so your agent never has to source or maintain a data feed.

Endpoint	Description	Price
POST /v1/live/volatility	Realized volatility (7d/30d/90d) + regime for a crypto asset, from fresh daily candles	$0.01
POST /v1/live/funding-rates	Current perpetual funding rate + annualized carry for a crypto asset	$0.005

curl -X POST https://api.quantoracle.dev/v1/live/volatility \
  -H "Content-Type: application/json" \
  -d '{"asset":"BTC"}'

# → {"asset":"BTC","spot":61728.7,"realized_vol_7d":0.4534,
#    "realized_vol_30d":0.3108,"realized_vol_90d":0.3157,"regime":"NORMAL",
#    "as_of_age_seconds":0,"stale":false,"source":"kraken", ...}

Pricing: the Live tier is paid from the first call — it is not part of the 1,000/day calculator free tier (the value is the fresh data + pipeline, which you can't replicate with a local library). You get 20 free calls per IP per day to evaluate, then it settles per-call via x402 (USDC on Base or Solana). You pay for freshness, not arithmetic.

Results are cached server-side (volatility ~5 min, funding ~1 min); if an upstream feed is briefly unavailable, the API serves the last good value flagged stale: true, with as_of_age_seconds telling you how fresh the answer is.

QuantOracle Watch — 24/7 position monitoring

Most monitoring agents rebuild the same loop: poll crypto/liquidation-price + risk/var-parametric on a timer, all day. Watch replaces the loop — register a crypto perp position once and an isolated watcher re-evaluates it every ~60 seconds: funding-adjusted liquidation distance (warn/critical bands with hysteresis), funding-rate sign flips, hourly vol-regime changes, and expiry warnings. Alerts fire as HMAC-signed webhooks (X-QO-Signature, key = your monitor token) and are recorded server-side, so the trial needs zero infrastructure — just poll.

Endpoint	Description	Price
POST /v1/watch/trial	Free 48-hour monitor — one per IP per 30 days	Free
POST /v1/watch/position	Register a position for 30 days of monitoring	$5.00
POST /v1/watch/extend	+30 days (also upgrades a trial; body: {monitor_id, token})	$5.00
PATCH /v1/watch/{id}	Update position params after you add margin / resize / move it	Free
GET /v1/watch/{id}	Live status + alert history (token auth)	Free
DELETE /v1/watch/{id}	Cancel	Free

curl -X POST https://api.quantoracle.dev/v1/watch/trial \
  -H "Content-Type: application/json" \
  -d '{"asset":"BTC","direction":"long","entry_price":62000,
       "position_size":5000,"collateral":1000}'

# → {"monitor_id":"w_...","token":"...","tier":"trial","status":"active",
#    "liquidation_price":49910,"distance_pct":19.5,
#    "status_url":"https://api.quantoracle.dev/v1/watch/w_...", ...}

No exchange keys, no custody, no execution — Watch reads public market data and sends webhooks, so the worst failure mode is a missed alert (the watcher heartbeat is published in /health as watcher_heartbeat_age_s). Webhook targets are SSRF-guarded and deliveries retried. The economics: a DIY loop polling the same math once a minute past the free tier costs ~$7.20/day in per-call fees vs $5 per 30 days. Full walkthrough: quantoracle.dev/writing/crypto-liquidation-alerts-for-agents.

x402 Payments

QuantOracle uses the x402 protocol for pay-per-call micropayments. When an agent exhausts its free tier (or calls a paid-only composite), the API returns a standard 402 response with payment instructions advertising both Base and Solana. x402-compatible agents (Coinbase AgentKit, AgentCash, OpenClaw, etc.) handle the rest automatically:

1. Agent calls endpoint, gets 402 with PAYMENT-REQUIRED header listing accepted networks
2. Agent signs a gasless USDC transfer authorization on Base (EIP-3009) or Solana
3. Agent resends request with PAYMENT-SIGNATURE header
4. Server verifies via CDP facilitator, serves the response, settles on-chain

No API keys. No subscriptions. No accounts. Just math and micropayments.

Supported Networks

Network	Asset	Gas	Best for
Base mainnet (eip155:8453)	USDC (0x8335...)	~$0.005/tx	EVM agents, Coinbase tooling, LangChain, Base ecosystem
Solana mainnet (solana:5eykt4...)	USDC (EPjFWdd5...)	~$0.0002/tx (CDP fee-payer)	Solana Agent Kit, Eliza, high-frequency bots

• Settlement: Via Coinbase Developer Platform facilitator (api.cdp.coinbase.com/platform/v2/x402)
• Base wallet: 0xC94f5F33ae446a50Ce31157db81253BfddFE2af6
• Solana wallet: 9biztrXscReJ3Wi8EfkD2gL3WXzYUmzTEohD26Bxp39u
• Discovery: https://api.quantoracle.dev/.well-known/x402 (returns both chains for every endpoint)

Test it with AgentCash

npx agentcash@latest onboard
# Fund the Base or Solana wallet shown, then:
npx agentcash fetch https://api.quantoracle.dev/v1/risk/full-analysis \
  -m POST --payment-network solana \
  --body '{"returns":[0.01,-0.02,0.03,0.005,-0.01,0.02,-0.015,0.025,0.01,-0.005,0.015]}'

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MCP Server

QuantOracle is available as a native MCP server with 80 tools (63 calculators + 11 composites + 2 live market-data endpoints + 3 QuantOracle Watch monitoring tools + batch). Works with Claude Desktop, Cursor, Windsurf, Smithery, and any MCP-compatible client.

Install via npm

npx quantoracle-mcp

Claude Desktop / Claude Code

Add as a connector in Settings, or add to claude_desktop_config.json:

{
  "mcpServers": {
    "quantoracle": {
      "url": "https://mcp.quantoracle.dev/mcp"
    }
  }
}

Or run locally via npx:

{
  "mcpServers": {
    "quantoracle": {
      "command": "npx",
      "args": ["-y", "quantoracle-mcp"]
    }
  }
}

Remote MCP (Streamable HTTP)

Connect directly to the hosted server — no install required:

https://mcp.quantoracle.dev/mcp

Smithery

npx @smithery/cli mcp add https://server.smithery.ai/QuantOracle/quantoracle

OpenClaw / ClawHub

clawhub install quantoracle

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Integrations

QuantOracle is available across multiple agent ecosystems:

Platform	How to connect
Claude Desktop / Claude Code	Connector URL: https://mcp.quantoracle.dev/mcp
Cursor / Windsurf	MCP config: npx quantoracle-mcp
Smithery	npx @smithery/cli mcp add QuantOracle/quantoracle
OpenClaw / ClawHub	clawhub install quantoracle
CLI	npm install -g quantoracle-cli or npx quantoracle-cli
Glama	glama.ai/mcp/servers/QuantOracledev/quantoracle
npm (MCP)	npx quantoracle-mcp
x402 ecosystem	x402.org/ecosystem
ChatGPT GPT	QuantOracle GPT
LangChain	pip install langchain-quantoracle
AgentCash	npx agentcash fetch https://api.quantoracle.dev/v1/...
x402scan	Server page — Base + Solana
REST API	https://api.quantoracle.dev/v1/...
OpenAPI spec	https://api.quantoracle.dev/openapi.json
Swagger UI	https://api.quantoracle.dev/docs

Tool Discovery

# List all tools (63 calculators + 10 composites) with paths and pricing
curl https://api.quantoracle.dev/tools

# x402 discovery (advertises Base + Solana for every endpoint)
curl https://api.quantoracle.dev/.well-known/x402

# Health check
curl https://api.quantoracle.dev/health

# Usage check
curl https://api.quantoracle.dev/usage

# MCP server card
curl https://mcp.quantoracle.dev/.well-known/mcp/server-card.json

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Full Endpoint Reference

Options (4 endpoints)

Endpoint	Description	Price
POST /v1/options/price	Black-Scholes pricing with 10 Greeks (delta through color)	$0.005
POST /v1/options/implied-vol	Newton-Raphson implied volatility solver	$0.005
POST /v1/options/strategy	Multi-leg options strategy P&L, breakevens, max profit/loss	$0.008
POST /v1/options/payoff-diagram	Multi-leg options payoff diagram data generation	$0.005

Derivatives (7 endpoints)