optionpricer 0.2.0

High-performance quantitative option pricing with Cython, Numba, and stochastic volatility models.

OptionPricer

A high-performance quantitative option pricing library with Cython AOT compilation, Numba JIT, stochastic volatility models, and institutional-grade numerical precision.

Installation

pip install optionpricer

For faster implied volatility (Jäckel's "Let's Be Rational"):

pip install optionpricer[fast]

Quick Start

from optionpricer import OptionContract, MarketState, black_scholes, build_tree

contract = OptionContract(strike=100, expiry=1.0, option_type="call")
market = MarketState(spot=100, rate=0.05, volatility=0.2)

# Analytical BSM (erfc-based, machine precision at ±8σ tails)
price = black_scholes(contract, market)

# American put via Cython binomial tree
put = OptionContract(strike=100, expiry=1.0, option_type="put", american=True)
american_price = build_tree(put, market, N=5000)

# Full Greek vector via closed-form AAD
from optionpricer import aad_greeks
greeks = aad_greeks(contract, market)
# -> {delta, gamma, vega, theta, rho, vanna, volga, charm}

Pricing Models

Model	Module	Style	Speed
Black-Scholes (erfc)	black_scholes()	European	~0.18 ms
Binomial Tree (Cython/OpenMP)	build_tree()	American/European	~0.3 ms (N=1000)
Crank-Nicolson FDM (Cython)	crank_nicolson_fdm()	American/European	~3.3 ms (200×200)
Monte Carlo (Sobol + CV)	monte_carlo_prices()	All	~1.0 ms (16K)
Merton Jump-Diffusion	merton_jump_diffusion()	European	~0.15 ms
Carr-Madan FFT	carr_madan_fft()	European	~0.23 ms
Heston Stochastic Vol	heston_price()	European	~0.5 ms
Bates SVJD	bates_price()	European	~0.5 ms
Quanto	quanto_price()	European	~0.1 ms
Multi-Asset Basket (MC)	basket_option()	European	~50 ms
Bjerksund-Stensland	bjerksund_stensland_american()	American	~0.1 ms
Barrier (Analytical)	barrier_analytical()	European	~0.1 ms

Analytics

Module	Function	Description
Implied Volatility	implied_vol()	Jäckel → Newton → Brent fallback
Greeks (BSM)	greeks()	Closed-form Euro, FD bumping American
AAD Greeks	aad_greeks()	Δ, Γ, V, Θ, ρ, Vanna, Volga, Charm
Malliavin MC Greeks	malliavin_greeks()	Smooth Greeks for non-diff payoffs
GARCH(1,1)	garch_fit()	MLE calibration with Numba variance path
EWMA Vol	ewma_volatility()	30-day fallback estimator
SABR Smile	sabr_implied_vol()	Hagan formula with edge guards
Dupire Local Vol	dupire_local_vol()	Surface from IV grid via spline
Vanna-Volga	vanna_volga_price()	Smile-adjusted exotic pricing
Nelson-Siegel	fit_nelson_siegel()	Yield curve calibration
Arbitrage Check	arbitrage_check()	Calendar + butterfly validation

Architecture

• Cython AOT: Binomial tree and FDM solvers compiled to C with OpenMP for multi-core parallelism
• Numba JIT: Monte Carlo paths, GARCH variance loop, Malliavin kernels compiled via LLVM
• erfc precision: All BSM CDF calls use erfc to maintain accuracy at extreme tails
• Pydantic V2: Type-safe contract/market schemas with validation

License

Apache 2.0 — see LICENSE.