Black-Scholes Pricer

A tested Black-Scholes options pricer with an implied-volatility solver (Newton-Raphson with Brent fallback), analytic Greeks, and arbitrage diagnostics.

Features

• Black-Scholes Pricing: European call/put options with continuous dividend yield
• Greeks Calculation: Delta, Gamma, Vega, Theta, Rho with numerical stability
• Implied Volatility: Newton-Raphson with Brent fallback for robust convergence
• Arbitrage Diagnostics: Put-call parity, price bounds, strike monotonicity, butterfly spreads
• CLI & Web UI: Professional command-line and Streamlit interfaces
• Tests: 93 tests (known-value, finite-difference, round-trip, and unit-convention checks)

Installation

git clone https://github.com/nolimitwaiz/black-scholes-pricer.git
cd black-scholes-pricer
pip install -e .

Quick Start

Python API

from src.core.black_scholes import black_scholes_call, calculate_greeks
from src.solvers.implied_vol import implied_volatility

# Price a call option
price = black_scholes_call(S=100, K=100, T=1.0, r=0.05, sigma=0.20, q=0.0)
print(f"Call price: ${price:.2f}")  # Call price: $10.45

# Calculate Greeks
greeks = calculate_greeks(S=100, K=100, T=1.0, r=0.05, sigma=0.20, option_type="call")
print(f"Delta: {greeks.delta:.4f}")  # Delta: 0.6368

# Solve for implied volatility
result = implied_volatility(market_price=10.45, S=100, K=100, T=1.0, r=0.05)
print(f"IV: {result.volatility:.2%}")  # IV: 20.00%

CLI

# Price an option
options-toolkit price -S 100 -K 100 -T 1.0 -r 0.05 -v 0.20 --type call

# Calculate Greeks
options-toolkit greeks -S 100 -K 100 -T 1.0 -r 0.05 -v 0.20

# Solve implied volatility
options-toolkit iv -p 10.45 -S 100 -K 100 -T 1.0 -r 0.05

Streamlit UI

streamlit run interfaces/streamlit_app.py

Architecture

Functional Core: Pure functions for all mathematical operations (pricing, Greeks) for maximum testability and clarity.

Hybrid Design: Optional thin class wrappers for convenience while maintaining functional purity in core logic.

Numerical Stability: Comprehensive edge case handling for T→0, σ→0, deep ITM/OTM scenarios.

Testing

# Run all tests
pytest

# With coverage
pytest --cov=src --cov-report=html

# Specific module
pytest tests/unit/test_black_scholes.py -v

Project Structure

black-scholes-pricer/
├── src/
│   ├── core/               # Black-Scholes pricing & Greeks
│   ├── solvers/            # Implied volatility (Newton-Raphson + Brent)
│   ├── diagnostics/        # Arbitrage checks
│   └── utils/              # Constants, types, distributions
├── interfaces/
│   ├── cli.py              # Command-line interface
│   └── streamlit_app.py    # Web UI
└── tests/                  # Test suite

License

MIT License - see LICENSE file

Author

Waiz Khan - GitHub