QuantOracle

<p align="center"> <h1 align="center">QuantOracle</h1> <p align="center"><strong>The quantitative computation API for autonomous financial agents</strong></p> <p align="center">63 deterministic, citation-verified calculators. 1,000 free calls/day. No signup.</p> </p>

<p align="center"> <a href="https://www.npmjs.com/package/quantoracle-mcp"><img src="https://img.shields.io/npm/v/quantoracle-mcp?label=npm&color=cb3837" alt="npm"></a> <a href="https://smithery.ai/server/QuantOracle/quantoracle"><img src="https://smithery.ai/badge/QuantOracle/quantoracle" alt="Smithery"></a> <a href="https://clawhub.ai"><img src="https://img.shields.io/badge/ClawHub-quantoracle-blueviolet" alt="ClawHub"></a> <a href="https://x402.org/ecosystem"><img src="https://img.shields.io/badge/x402-USDC%20on%20Base-0052FF" alt="x402"></a> <a href="https://opensource.org/licenses/MIT"><img src="https://img.shields.io/badge/license-MIT-blue" alt="MIT License"></a> </p>

<p align="center"> <a href="https://quantoracle.dev">quantoracle.dev</a>  |  <a href="#mcp-server">MCP Server</a>  |  <a href="#x402-payments">x402 Payments</a>  |  <a href="#free-tier">Free Tier</a>  |  <a href="#full-endpoint-reference">All 63 Endpoints</a>  |  <a href="#integrations">Integrations</a> </p>

---

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"}'

{
  "call_price": 3.6862,
  "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()["call_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={
    "S0": 10000, "mu": 0.08, "sigma": 0.15, "T": 10, "simulations": 1000
})
print(r.json()["median_terminal"])  # 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 { call_price, delta, gamma, vega } = await res.json();

---

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.