diffuse

Quantitative Finance Engine — Heat Equation PDE Option Pricing & Prediction Market Data

Diffuse prices European, American, and barrier options by solving the Black-Scholes PDE via a transformation to the heat equation. It then applies finite-difference numerical schemes (Crank-Nicolson, FTCS, BTCS) to compute prices, full Greeks, and 3D price surfaces. Includes a pricing web UI, REST API, WebSocket streaming, CLI, and Docker deployment.

Diffuse also provides public API clients for Manifold Markets and Polymarket market data.

Features

Domain	Feature
Option Pricing	European calls/puts, American puts (early exercise), Barrier (knock-out) options
Numerical Methods	Crank-Nicolson (2nd-order, default), BTCS (implicit), FTCS (explicit)
Risk Analytics	Full Greeks — Delta, Gamma, Theta, Vega, Rho via finite differences
Visualization	3D Interactive price surface (strike × maturity), pricing history chart
Pricing UI	React + Tailwind terminal-style dashboard with WebSocket streaming
Prediction Markets	Manifold Markets & Polymarket API clients with normalized probability history
API	FastAPI REST with RS256 JWT auth, auto-generated Swagger docs
CLI	Click-based command-line interface for batch pricing and market-data inspection
Deployment	Docker Compose (nginx + API + Postgres + Redis)

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Quick Start — Web UI

# 1. Start the API server
uvicorn diffuse.api.main:app --host 127.0.0.1 --port 8000

# 2. Start the frontend (separate terminal)
cd frontend && npm install && npm run dev

Open http://localhost:5173, enter your JWT Bearer token, set parameters, and click PRICE.

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Quick Start — CLI

# Install the package
pip install -e .

# Price a European call
diffuse price --S0 100 --K 100 --sigma 0.2 --T 1.0

# Get Greeks as JSON
diffuse greeks --S0 100 --K 100 --sigma 0.2 --T 1.0 --json

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Quick Start — Python

from diffuse.finance.greeks import compute_all_greeks

greeks = compute_all_greeks(S0=100, K=100, r=0.05, q=0.0, sigma=0.2, T=1.0)

for name, value in greeks.items():
    print(f"{name:>6s}: {value:.10f}")
# Output:
#  delta: 0.6368306512
#  gamma: 0.0187618023
#  theta: -1.0907789103
#   vega: 0.3752360448
#    rho: 0.5325399913

---

Docker Deployment

# Full stack (API + nginx + Postgres + Redis)
docker compose -f docker/docker-compose.yml up --build

The app will be available at http://localhost. The nginx reverse proxy handles:

• Static frontend files
• API requests via /api/*
• WebSocket connections via /ws/*

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Frontend Deployment (Vercel)

See deploy_app_into.md for step-by-step Vercel deployment instructions.

Quick summary:

Setting	Value
Framework	Vite
Root directory	frontend
Build command	npm run build
Output directory	dist
Install command	npm install

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REST API

Start the server:

uvicorn diffuse.api.main:app --host 0.0.0.0 --port 8000

Endpoints

Method	Path	Auth	Description
POST	/price	JWT	Price an option — returns price + Greeks
POST	/greeks	JWT	Compute Greeks only
POST	/surface	JWT	Compute price surface (strike × maturity grid)
GET	/health	—	Health check
GET	/metrics	—	Prometheus metrics
WS	/ws/price?token=<jwt>	JWT	WebSocket live pricing stream

Swagger docs at http://localhost:8000/docs.

Example — POST /price

// Request
{
  "option_type": "european_call",
  "S0": 100, "K": 100, "sigma": 0.2, "T": 1.0,
  "r": 0.05, "q": 0.0, "scheme": "cn",
  "N_x": 500, "N_t": 500
}

// Response
{
  "price": 10.4505835722,
  "greeks": {
    "delta": 0.6368306512,
    "gamma": 0.0187618023,
    "theta": -1.0907789103,
    "vega": 0.3752360448,
    "rho": 0.5325399913
  },
  "scheme_used": "cn",
  "courant_number": 0.499002,
  "request_id": "abc123..."
}

---

CLI Reference

# Price an option
diffuse price --S0 100 --K 100 --sigma 0.2 --T 1.0

# With all options
diffuse price --S0 100 --K 100 --sigma 0.3 --T 1.0 \
  --type american_put --scheme cn --N-x 501 --N-t 501 --json

# Compute Greeks
diffuse greeks --S0 100 --K 100 --sigma 0.2 --T 1.0 --json

# Start API server
diffuse serve --host 0.0.0.0 --port 8000 --reload

---

Configuration

Set via environment variables or .env file:

Variable	Default	Description
JWT_PUBLIC_KEY_PEM	(required)	RS256 public key
JWT_PRIVATE_KEY_PEM	(required)	RS256 private key
ALLOWED_ORIGINS	["http://localhost:3000"]	CORS origins
LOG_LEVEL	INFO	Logging level

Generate keys:

bash scripts/generate_keys.sh

---

Development

pip install -r requirements-dev.txt
pytest tests/ -v --cov=src/diffuse --cov-report=term-missing
ruff check src/
mypy src/

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Architecture

src/diffuse/
├── solver/          # PDE: grid, FTCS/BTCS/CN schemes, solver
├── finance/         # Black-Scholes transform, payoffs, Greeks
├── markets/         # Manifold Markets & Polymarket API clients
│   ├── manifold.py  #   → api.manifold.markets/v0
│   ├── polymarket.py #  → clob.polymarket.com
├── api/             # FastAPI (routes, auth, audit, WebSocket)
├── cli/             # Click CLI
└── config.py        # Environment config

frontend/
├── src/
│   ├── App.tsx                # Main app with QF branding
│   ├── components/            # UI components
│   │   ├── ApiKeyInput.tsx
│   │   ├── HowItWorks.tsx      # Algorithm explainer
│   │   ├── ParamsForm.tsx
│   │   ├── PriceDisplay.tsx
│   │   ├── TradeChart.tsx
│   │   ├── GreeksPanel.tsx
│   │   └── SurfacePlot3D.tsx
│   ├── hooks/
│   │   └── useWebSocket.ts    # WS with auto-reconnect
│   └── types.ts
└── ...                        # Vite + Tailwind config

Pricing Pipeline

BS params → heat transform → initial condition → PDE solve → inverse transform → price + Greeks

Prediction Market Pipeline

Market API → response parsing → normalized probability history

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License

Proprietary. All rights reserved.