optionpricer 0.1.5

A high-performance, professional-grade (i tried) quantitative option pricing library with Numba and Cython optimizations.

OptionPricer

A high-performance, professional-grade (to the best of my ability) quantitative finance library for option pricing, optimized heavily via NumPy vectorization, Numba JIT, and Cython AOT compilation.

Development Journey & Architecture

This package was built systematically through strict, high-performance architectural phases:

1. Phase 1: NumPy Vectorization

   • Eliminated slow Python loops in the core hot paths.
   • Replaced scalar stock price reconstructions with precomputed power arrays, yielding a 3.7x baseline speedup on the binomial lattice.

2. Phase 2: Advanced Monte Carlo & Variance Reduction

   • Implemented Sobol Quasi-Random sequences to ensure superior space-filling over standard pseudo-random engines.
   • Introduced Antithetic Variates ($Z$ and $-Z$) and Control Variates (using terminal spot price correlation) to achieve up to 800x variance reduction, allowing high precision at drastically lower path counts.

3. Phase 3: Numba JIT Compilation

   • Compiled the sequential backward-induction algorithms into machine code via LLVM.
   • Handled Python's GIL overhead by isolating numerical loops inside pure-C equivalents, dropping execution time from 48ms down to 5ms for large $N$.

4. Phase 4: Cython Extensions & Pre-compiled Wheels

   • Statically typed the core mathematical functions (cdef, double[:] memoryviews) into an AOT compiled C-extension to completely eliminate runtime compilation warmup.

5. Phase 5: Algorithmic Routing

   • Engineered smart heuristics for implied volatility. Routes to Peter Jäckel's 'Let's Be Rational' for standard Euro options, falls back to Newton-Raphson for near-ATM scenarios, and seamlessly redirects to SciPy's robust brentq for deep OTM/ITM and American edge cases.

6. Phase 6: Professional Software Engineering

   • Enforced strict dependency boundaries.
   • Fully annotated with Python Type Hints and Google-style docstrings.
   • Prepared for distribution via PyPA build and twine CI/CD standards.

Performance Benchmarks

• Black-Scholes (Analytical): ~0.028 ms
• Implied Volatility (Brentq Solver): ~0.144 ms
• Binomial Tree (American, N=1000): ~0.362 ms
• Monte Carlo (Optimized, N=32,768): ~0.519 ms
• Binomial Tree (American, N=5000): ~6.766 ms

Usage

pip install optionpricer

from optionpricer import build_tree, monte_carlo_prices, implied_vol

# Price a 5,000-step American Put via Cython
price = build_tree(S=100, K=100, T=1, r=0.05, sigma=0.2, N=5000, option_type="put", american=True)

# Generate 32,000 variance-reduced Monte Carlo paths
mc_price = monte_carlo_prices(S=100, K=100, T=1, r=0.05, sigma=0.2)