derivatives-pricing

A Python package for options pricing and Greeks computation, with a unified API across analytical, binomial tree, finite difference and Monte Carlo methods.

Built for teaching, research, and production-adjacent workflows.

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Features

Pricing Coverage

	Vanilla	Asian	Barrier	Custom
BSM	E	E	E	—
Binomial	E/A	E/A	E/A	E/A
PDE_FD	E/A	—	E/A	E/A
Monte Carlo	E/A	E/A	E/A	E/A

E = European, A = American

Method details: BSM uses closed-form Black-Scholes-Merton; Binomial uses Cox-Ross-Rubinstein trees; PDE_FD supports implicit, explicit, and Crank-Nicolson finite difference schemes; Monte Carlo uses Longstaff-Schwartz for American-style exercise. Asian analytical pricing uses Turnbull-Wakeman (arithmetic) and Kemna-Vorst (geometric), with Hull averaging on binomial trees. Barrier pricing supports continuous and discrete monitoring, knock-in and knock-out structures, and rebates.

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Additional Capabilities

• Greeks — analytical, tree, grid, pathwise, likelihood-ratio, and numerical bump-and-revalue (delta, gamma, vega, theta, rho)
• Implied volatility — Newton-Raphson, bisection, and Brent solvers with arbitrage-bounds checking
• Stochastic processes — Geometric Brownian Motion, Jump Diffusion (Merton), Square-Root Diffusion (CIR)
• Discount curves — log-linear interpolation on arbitrary term structures; deterministic time-varying forward rate and dividend curves
• Discrete dividends — supported across all pricing methods
• Control variates — European analytical control variates for American pricing variance reduction
• Custom payoffs — user-defined payoff functions via PayoffSpec

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Why derivatives-pricing?

• Consistent API across analytical, tree, finite difference, and Monte Carlo methods
• Designed for transparency and clarity of implementation
• Includes vanilla, Asian, barrier, and custom-payoff workflows behind the same facade
• Suitable for teaching, experimentation, research, and production-adjacent workflows
• Extensible architecture for new models and payoffs

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Installation

Install from PyPI:

pip install derivatives-pricing
# or pip install derivatives-pricing[numba] for optional PDE_FD solver acceleration

Beta feature — barrier options

Barrier option pricing is currently available as a pre-release. To install:

pip install --pre -U derivatives-pricing

For development:

pip install -r requirements/dev.txt   
pip install -e . --no-deps                                                                         
pip install -e ".[jupyter]"           # optional, for running notebooks

Requires Python 3.10 – 3.13

Quick Start

import datetime as dt

import derivatives_pricing as dp

pricing_date = dt.datetime(2025, 1, 1)
maturity = dt.datetime(2025, 7, 1)

dc = dp.DiscountCurve.flat(rate=0.05)
md = dp.MarketData(
    pricing_date=pricing_date,
    discount_curve=dc,
    currency="USD",
)

underlying = dp.UnderlyingData(
    initial_value=100.0,
    volatility=0.20,
    market_data=md,
)

spec = dp.VanillaSpec(
    option_type=dp.OptionType.CALL,
    exercise_type=dp.ExerciseType.EUROPEAN,
    strike=105.0,
    maturity=maturity,
)

val = dp.OptionValuation(
    underlying=underlying,
    spec=spec,
    pricing_method=dp.PricingMethod.BSM,
)
print(f"{'PV:':<8} {val.present_value():>10.4f}")
print(f"{'Delta:':<8} {val.delta():>10.4f}")

Examples & Tutorials

The repo includes two companion directories:

• examples/ — concise notebooks showing how to call the public API for each feature (European and American vanilla options, Asians, barriers, Greeks, jump diffusion, discount curves).
• tutorials/ — deeper walkthroughs that teach the theory behind each pricing method (BSM, binomial trees, finite differences, Monte Carlo, Asian averaging, barrier pricing). Tutorials may access private/internal classes for demonstration purposes.

Tests

pytest -q -n auto --runslow

Project Structure

src/derivatives_pricing/
├── enums.py                  # OptionType, ExerciseType, PricingMethod, …
├── exceptions.py             # Custom exception hierarchy
├── market_environment.py     # MarketData, CorrelationContext
├── rates.py                  # DiscountCurve (log-linear interpolation)
├── stochastic_processes.py   # GBM, JDProcess, SRD, PathSimulation
├── utils.py                  # Day-count, forward price, put-call parity
├── valuation/
│   ├── asian_analytical.py   # Turnbull-Wakeman, Kemna-Vorst
│   ├── barrier_analytical.py # Analytical barrier pricing
│   ├── binomial.py           # Cox-Ross-Rubinstein tree
│   ├── bsm.py                # Closed-form Black-Scholes-Merton
│   ├── contracts.py          # VanillaSpec, BarrierSpec, PayoffSpec, AsianSpec
│   ├── core.py               # OptionValuation facade, UnderlyingData
│   ├── implied_volatility.py # IV solver
│   ├── monte_carlo.py        # Monte Carlo with Longstaff-Schwartz and barrier pricing
│   ├── params.py             # MonteCarloParams, BinomialParams, PDEParams
│   └── pde.py                # Finite difference (implicit, explicit, Crank-Nicolson, barriers)
tests/                        # Test suite
examples/                     # API usage notebooks
tutorials/                    # Theory deep-dive notebooks

Found a bug or have a feature request? Open an issue.

Disclaimer

This pricing library is provided as-is. Users are responsible for independently verifying any results before relying on them.

License

This repository uses a dual-license model.

Component	License	SPDX
src/derivatives_pricing/	MIT	MIT
examples/	MIT	MIT
tutorials/	CC BY-NC-SA 4.0	CC-BY-NC-SA-4.0

Library code and examples are released under the MIT License and may be freely used, modified, and redistributed.

The PyPI distribution contains the MIT-licensed library package. Tutorial materials are separately hosted in the GitHub repository and are not part of the published package.

Tutorial notebooks in tutorials/ are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC BY-NC-SA 4.0). You may share and adapt these materials for non-commercial purposes with attribution. See the full license text for details.