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QuantOracle

The quantitative computation API for autonomous financial agents

63 deterministic, citation-verified calculators. 1,000 free calls/day. No signup.

npm Smithery ClawHub x402 MIT License

quantoracle.dev  |  MCP Server  |  x402 Payments  |  Free Tier  |  All 63 Endpoints  |  Integrations

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
  • Zero dependencies on market data, accounts, or third-party APIs -- send numbers in, get numbers out
  • Deterministic -- same inputs always produce the same outputs, 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
  • Sub-millisecond response times on most endpoints
  • 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.

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": 3.6862,
  "greeks": {
    "delta": 0.4467,
    "gamma": 0.0281,
    "theta": -0.0113,
    "vega": 0.2653,
    "rho": 0.1989
  },
  "d1": -0.1331,
  "d2": -0.2745,
  "ms": 0.04
}

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"])  # 3.6862

# 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()["sharpe_ratio"])  # Annualized Sharpe

# Kelly Criterion
r = requests.post("https://api.quantoracle.dev/v1/risk/kelly", json={
    "win_prob": 0.55, "win_loss_ratio": 1.5
})
print(r.json()["kelly_fraction"])  # Optimal bet size

# 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;

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
Endpoints All 63 All 63
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

x402 Payments

QuantOracle uses the x402 protocol for pay-per-call micropayments. When an agent exhausts its free tier, the API returns a standard 402 response with payment instructions. x402-compatible agents (Coinbase AgentKit, OpenClaw, etc.) handle this automatically:

  1. Agent calls endpoint, gets 402 with PAYMENT-REQUIRED header
  2. Agent signs a gasless USDC transfer authorization (EIP-3009)
  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.

  • Currency: USDC on Base (chain ID 8453)
  • Settlement: Via Coinbase Developer Platform facilitator
  • Wallet: 0xC94f5F33ae446a50Ce31157db81253BfddFE2af6

MCP Server

QuantOracle is available as a native MCP server with 63 tools. Works with Claude Desktop, Cursor, Windsurf, 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

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
npm npx quantoracle-mcp
x402 ecosystem x402.org/ecosystem
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 63 tools with paths and pricing
curl https://api.quantoracle.dev/tools

# 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

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)

Endpoint Description Price
POST /v1/derivatives/binomial-tree CRR binomial tree pricing for American and European options $0.008
POST /v1/derivatives/barrier-option Barrier option pricing using analytical formulas $0.008
POST /v1/derivatives/asian-option Asian option pricing: geometric closed-form or arithmetic approximation $0.008
POST /v1/derivatives/lookback-option Lookback option pricing (floating/fixed strike, Goldman-Sosin-Gatto) $0.008
POST /v1/derivatives/option-chain-analysis Option chain analytics: skew, max pain, put-call ratios $0.015
POST /v1/derivatives/put-call-parity Put-call parity check and arbitrage detection $0.002
POST /v1/derivatives/volatility-surface Build implied volatility surface from market data $0.015

Risk (8 endpoints)

Endpoint Description Price
POST /v1/risk/portfolio 22 risk metrics: Sharpe, Sortino, Calmar, Omega, VaR, CVaR, drawdown $0.008
POST /v1/risk/kelly Kelly Criterion: discrete (win/loss) or continuous (returns series) $0.005
POST /v1/risk/position-size Fixed fractional position sizing with risk/reward targets $0.005
POST /v1/risk/drawdown Drawdown decomposition with underwater curve $0.005
POST /v1/risk/correlation N x N correlation and covariance matrices from return series $0.008
POST /v1/risk/var-parametric Parametric Value-at-Risk and Conditional VaR $0.008
POST /v1/risk/stress-test Portfolio stress test across multiple scenarios $0.008
POST /v1/risk/transaction-cost Transaction cost model: commission + spread + Almgren market impact $0.005

Indicators (6 endpoints)

Endpoint Description Price
POST /v1/indicators/technical 13 technical indicators (SMA, EMA, RSI, MACD, etc.) + composite signals $0.005
POST /v1/indicators/regime Trend + volatility regime + composite risk classification $0.005
POST /v1/indicators/crossover Golden/death cross detection with signal history $0.005
POST /v1/indicators/bollinger-bands Bollinger Bands with %B, bandwidth, and squeeze detection $0.002
POST /v1/indicators/fibonacci-retracement Fibonacci retracement and extension levels $0.002
POST /v1/indicators/atr Average True Range with normalized ATR and volatility regime $0.002

Statistics (10 endpoints)

Endpoint Description Price
POST /v1/stats/linear-regression OLS linear regression with R-squared, t-stats, standard errors $0.008
POST /v1/stats/polynomial-regression Polynomial regression of degree n with goodness-of-fit metrics $0.008
POST /v1/stats/cointegration Engle-Granger cointegration test with hedge ratio and half-life $0.008
POST /v1/stats/hurst-exponent Hurst exponent via rescaled range (R/S) analysis $0.008
POST /v1/stats/garch-forecast GARCH(1,1) volatility forecast using maximum likelihood estimation $0.015
POST /v1/stats/zscore Rolling and static z-scores with extreme value detection $0.002
POST /v1/stats/distribution-fit Fit data to common distributions and rank by goodness of fit $0.008
POST /v1/stats/correlation-matrix Correlation and covariance matrices with eigenvalue decomposition $0.015
POST /v1/stats/realized-volatility Realized vol: close-to-close, Parkinson, Garman-Klass, Yang-Zhang $0.005
POST /v1/stats/normal-distribution Normal distribution: CDF, PDF, quantile, confidence intervals $0.002
POST /v1/stats/sharpe-ratio Standalone Sharpe ratio with Lo (2002) standard error and 95% CI $0.002
POST /v1/stats/probabilistic-sharpe Probabilistic Sharpe Ratio (Bailey & Lopez de Prado 2012) $0.005

Portfolio (2 endpoints)

Endpoint Description Price
POST /v1/portfolio/optimize Portfolio optimization: max Sharpe, min vol, or risk parity $0.015
POST /v1/portfolio/risk-parity-weights Equal risk contribution portfolio weights (Spinu 2013) $0.008

Fixed Income (4 endpoints)

Endpoint Description Price
POST /v1/fixed-income/bond Bond price, Macaulay/modified duration, convexity, DV01 $0.008
POST /v1/fixed-income/amortization Full amortization schedule with extra payment savings analysis $0.005
POST /v1/fi/yield-curve-interpolate Yield curve interpolation: linear, cubic spline, Nelson-Siegel $0.015
POST /v1/fi/credit-spread Credit spread and Z-spread from bond price vs risk-free curve $0.008

Crypto / DeFi (7 endpoints)

Endpoint Description Price
POST /v1/crypto/impermanent-loss Impermanent loss calculator for Uniswap v2/v3 AMM positions $0.005
POST /v1/crypto/apy-apr-convert Convert between APY and APR with configurable compounding $0.002
POST /v1/crypto/liquidation-price Liquidation price calculator for leveraged positions $0.002
POST /v1/crypto/funding-rate Funding rate analysis with annualization and regime detection $0.005
POST /v1/crypto/dex-slippage DEX slippage estimator for constant-product AMM (x*y=k) $0.005
POST /v1/crypto/vesting-schedule Token vesting schedule with cliff, linear/graded unlock, TGE $0.005
POST /v1/crypto/rebalance-threshold Portfolio rebalance analyzer: drift detection and trade sizing $0.005

FX / Macro (7 endpoints)

Endpoint Description Price
POST /v1/fx/interest-rate-parity Interest rate parity calculator with arbitrage detection $0.005
POST /v1/fx/purchasing-power-parity Purchasing power parity fair value estimation $0.005
POST /v1/fx/forward-rate Bootstrap forward rates from a spot yield curve $0.005
POST /v1/fx/carry-trade Currency carry trade P&L decomposition $0.005
POST /v1/macro/inflation-adjusted Nominal to real returns using Fisher equation $0.002
POST /v1/macro/taylor-rule Taylor Rule interest rate prescription $0.002
POST /v1/macro/real-yield Real yield and breakeven inflation from nominal yields $0.002

Time Value of Money (5 endpoints)

Endpoint Description Price
POST /v1/tvm/present-value Present value of a future lump sum and/or annuity stream $0.002
POST /v1/tvm/future-value Future value of a present lump sum and/or annuity stream $0.002
POST /v1/tvm/irr Internal rate of return via Newton-Raphson $0.005
POST /v1/tvm/npv Net present value with profitability index and payback period $0.002
POST /v1/tvm/cagr Compound annual growth rate with forward projections $0.002

Simulation (1 endpoint)

Endpoint Description Price
POST /v1/simulate/montecarlo GBM Monte Carlo with contributions/withdrawals, up to 5000 paths $0.015

Example: Agent Backtest Workflow

A typical agent backtest chains multiple QuantOracle calls per iteration:

1. /v1/indicators/technical    -- generate signals (SMA, RSI, MACD)
2. /v1/risk/position-size      -- size the trade (fixed fractional)
3. /v1/risk/transaction-cost   -- estimate execution costs
4. /v1/options/price            -- price the hedge (Black-Scholes)
5. /v1/risk/portfolio           -- compute running Sharpe, drawdown, VaR
6. /v1/stats/probabilistic-sharpe -- is the Sharpe statistically significant?
7. /v1/tvm/cagr                 -- compute CAGR of the equity curve

Each call is a pure calculator -- no state, no side effects, no API keys.

Self-Hosting

# Clone and run locally
git clone https://github.com/QuantOracledev/quantoracle.git
cd quantoracle
pip install fastapi uvicorn
uvicorn api.quantoracle:app --host 0.0.0.0 --port 8000

# Docker
docker compose up -d

# Docs at http://localhost:8000/docs

Accuracy

Every endpoint is tested against published analytical solutions:

  • 120 citation-backed benchmarks (Hull, Wilmott, Bailey & Lopez de Prado, Goldman-Sosin-Gatto, Taylor, Fisher, Markowitz)
  • 65 integration tests covering all 63 endpoints
  • Pure Python math -- no numpy/scipy, zero native dependencies
  • Deterministic: same inputs always produce the same outputs

Run the verification suite yourself:

python tests/accuracy_benchmarks.py https://api.quantoracle.dev

Architecture

quantoracle/
  api/quantoracle.py        -- FastAPI app, 63 endpoints, pure Python math
  worker/src/index.ts        -- Cloudflare Worker: rate limiting + x402 payments
  mcp-server/src/index.ts    -- MCP server: 63 tools over Streamable HTTP
  mcp-server/SKILL.md        -- ClawHub skill definition
  openapi.json               -- OpenAPI 3.0 spec
  tests/
    test_all.py              -- 65 integration tests
    accuracy_benchmarks.py   -- 120 citation-backed accuracy tests

Stack: FastAPI + Pydantic | Cloudflare Workers + KV | MCP (Streamable HTTP) | x402 + CDP Facilitator | USDC on Base

License

MIT -- use QuantOracle however you want.

About

63 deterministic quant computation tools for autonomous financial agents. Options, derivatives, risk, portfolio, statistics, crypto/DeFi, macro/FX, TVM. 1,000 free calls/day — no signup.

quantoracle.dev

Topics

finance crypto mcp monte-carlo derivatives portfolio-optimization quantitative-finance black-scholes risk-management financial-calculator backtesting options-pricing defi fastapi agent-tools x402

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