QuantOracle

The quantitative computation API for autonomous financial agents

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

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

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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
• 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
• 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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Add QuantOracle to Your Agent

Drop this into your agent's system prompt:

You have access to QuantOracle -- 63 deterministic financial calculators 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

Full endpoint list: https://api.quantoracle.dev/tools
OpenAPI spec: https://api.quantoracle.dev/openapi.json

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

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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 endpoints 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

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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
Composite	$0.015-0.05	Spread scan, regime classify, full analysis, trade evaluate, portfolio health, pairs signal (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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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

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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

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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
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 (12 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

Composite Endpoints (paid-only)

Higher-level endpoints that combine multiple calculations into a single call. Same math as the individual endpoints -- just packaged for common agent workflows. No free tier.

Endpoint	Description	Replaces	Price
POST /v1/options/spread-scan	Scan and rank vertical spreads by risk/reward	8-16 options/price calls	$0.05
POST /v1/indicators/regime-classify	Trend, vol regime, RSI, direction, strategy suggestion	technical + regime + realized-vol	$0.015
POST /v1/risk/full-analysis	Complete risk tearsheet: Sharpe, Sortino, VaR, Kelly, drawdown, Hurst, CAGR	7 individual calls	$0.04
POST /v1/trade/evaluate	Trade evaluation: sizing, risk/reward, Kelly, costs, regime, signals, verdict	5 individual calls	$0.025
POST /v1/portfolio/health	Portfolio health check: risk, correlation, rebalance, stress test	6 individual calls	$0.04
POST /v1/pairs/signal	Pairs trading signal: cointegration, Hurst, z-score, half-life, hedge ratio	4 individual calls	$0.025

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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.

Strategy Optimizer (1,200+ calls)

examples/strategy_optimizer.py is a full walk-forward parameter optimizer that demonstrates heavy API usage:

Phase	What it does	API calls
Parameter Sweep	Test 180 lookback/rebalance/RSI combinations across 8 assets	~1,080
Deep Analysis	22 risk metrics + VaR + Kelly + Monte Carlo on top 3 configs	~60-80
Options Overlay	Price covered calls across 6 assets x 4 expiries x 5 strikes	~100-150
Pairs Analysis	Cointegration scan + Hurst exponent on 45 asset pairs	~50-70

pip install requests
python examples/strategy_optimizer.py

A single run makes ~1,200-1,500 API calls. At paid rates that's ~$6-8 USDC. The same calculations done by an LLM in-context would cost $12-60 in tokens (Sonnet to Opus), take 4x longer, and get 15-30% of the complex math wrong.

---

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
  cli/                       -- quantoracle-cli: 63 tools in the terminal (npm)
  tests/
    test_integration.py      -- 65 integration tests (all endpoints, live API)
    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.