derivatives-pricing 0.1.0

Python package for options pricing and Greeks computation

derivatives-pricing

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

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

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Features

Pricing Coverage

	Vanilla		Asian		Custom
Method	European	American	European	American	European	American
BSM	✅	—	✅	—	—	—
Binomial	✅	✅	✅	✅	✅	✅
PDE	✅	✅	—	—	—	—
Monte Carlo	✅	✅	✅	✅	✅	✅

Method details: BSM uses closed-form Black-Scholes-Merton; Binomial uses Cox-Ross-Rubinstein trees; PDE 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.

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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, PDE, and Monte Carlo methods
• Designed for transparency and clarity of implementation
• 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

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, end_time=1.0)
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 options, Americans, PDE, Asian, Greeks, jump diffusion, discount curves).
• tutorials/ — deeper walkthroughs that teach the theory behind each pricing method (binomial trees, finite differences, Monte Carlo, Asian averaging). Tutorials may access private/internal classes for demonstration purposes.

Tests

pytest -q

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
│   ├── binomial.py           # Cox-Ross-Rubinstein tree
│   ├── bsm.py                # Closed-form Black-Scholes-Merton
│   ├── contracts.py          # VanillaSpec, PayoffSpec, AsianSpec
│   ├── core.py               # OptionValuation facade, UnderlyingData
│   ├── implied_volatility.py # IV solver
│   ├── monte_carlo.py        # Monte Carlo with Longstaff-Schwartz
│   ├── params.py             # MonteCarloParams, BinomialParams, PDEParams
│   └── pde.py                # Finite difference (implicit, explicit, Crank-Nicolson)
tests/                        # Test suite
examples/                     # API usage notebooks
tutorials/                    # Theory deep-dive notebooks

Disclaimer

This library is provided for educational, research, and exploratory use. While care has been taken in implementation and testing, it has not undergone the independent audit or regulatory validation expected of production trading systems. Users are responsible for verifying results before use in financial decision-making.

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.