American Options Pricer

Traders@SMU · HW 1. Black-Scholes-Merton, American binomial tree, Longstaff-Schwartz Monte Carlo, Greeks, implied volatility and volatility surfaces, as a Python package, a CLI and a website.

Live site: https://ferrsir.github.io/options-pricer/

What's here

HW requirement	Where
BSM pricer (+ dividend yield)	src/pricer/bsm.py
American options pricer (CRR tree, exercise-vs-continue at each node)	src/pricer/binomial.py
LSMC (regression on basis functions, compare to the tree)	src/pricer/lsmc.py
Greeks + visualizations (stretch)	bsm_greeks, viz.py, Greeks tab on the site
Slide sanity checks	checks.py, 31 tests in tests/
Implied vol from a market premium	implied_vol, Your premium box on the site
Vol-surface picture from Yahoo Finance	python -m pricer surface NDX
Ticker → Yahoo data	data.py + site
How every number is derived	METHODOLOGY.md
Plain-English explanation of every term, number and graph	GUIDE.md (also the Guide tab on the site)
Type your own premium and see what happens	Your premium box, banner and What-if tab on the site

Quick start

git clone https://github.com/Ferrsir/options-pricer && cd options-pricer
python -m venv .venv && .venv\Scripts\activate      # macOS/Linux: source .venv/bin/activate
pip install -e ".[dev]"
python -m pytest -q                                   # 31 tests

Price an option

# manual inputs: 1y ATM put, 5% rate, 20% vol; American tree + LSMC + charts
python -m pricer price --spot 100 --strike 100 --years 1 --rate 0.05 --vol 0.2 --type put --lsmc --out output/put

# from a ticker (spot, rate, dividend yield, historical vol pulled from Yahoo Finance)
python -m pricer price --ticker AAPL --strike 340 --days 30 --type call

# you saw a premium in the market: solve implied vol and price with it
python -m pricer price --ticker AAPL --strike 340 --days 30 --type call --premium 9.25
python -m pricer iv --premium 9.25 --spot 335 --strike 340 --days 30 --rate 0.04

Sample output (S=K=100, T=1, r=5%, σ=20% put):

BSM (European, closed form)         5.5735
European tree (1000 steps)          5.5715   (error vs BSM -0.00200)
American tree (1000 steps)          6.0896   (early-exercise premium +0.5181)
American LSMC (100000 paths)        6.0608   (± 0.0440 95% CI; biased slightly low)

Volatility surface picture

python -m pricer surface NDX --out output/ndx_surface.png     # any ticker with listed options
python -m pricer surface --demo                               # synthetic data, works offline

Sanity checks from the slide

python -m pricer checks

Run the website locally with live data for any ticker

python -m pricer serve          # http://localhost:8000

The website

docs/ is a static site (plain JS + Plotly, no build step) served by GitHub Pages. The pricing engine is re-implemented in JavaScript and agrees with Python to ~1e-12.

• Inputs for S, K, expiry, σ, r, q; call/put, long/short, European/American
• Glass-style UI with a start-here guide, one-click examples, info tooltips, keyboard-navigable tabs, and a Copy link button that restores your exact inputs from the URL
• Type or drag a premium: edge vs the model, implied vol, breakeven, P(profit), max gain/loss; a Recommended premium that is pre-filled when you load a stock (type your own to see everything react), and a switch that puts the Greeks, the 3-D Greek surface, payoff, What-if and a vol-surface marker at either your σ or the σ your premium implies (Greeks tab overlays both)
• Premium impact tab: model-vs-market comparison of σ and every Greek, plus curves showing how each number reacts as the premium changes (e.g. "model says 105, market says 150")
• What-if tab: move spot, volatility and days and see your P&L, a Greek waterfall of where it came from, and a P&L heat map
• Overview (BSM / European tree / American tree / LSMC), Greeks (charts vs spot, time, vol and a 3-D Greek surface), payoff diagram, tree convergence and early-exercise boundary, interactive 3-D vol surface, live sanity checks, and the derivation

Ticker data: any optionable US ticker. Neither Yahoo Finance nor Cboe can be called from a web page (no CORS), so the site talks to a small API and degrades gracefully:

1. python -m pricer serve on your machine: Yahoo Finance first, Cboe's public delayed chains as the automatic fallback; the vol surface is built in Python.
2. The serverless API in serverless/ (standard-library Python, Cboe data): quotes, chains and a compact multi-expiry payload. The browser builds the vol surface itself (docs/js/surface.js, a port of the Python pipeline, checked against it to ~1e-13). It is deployed on Vercel (https://options-pricer-api-five.vercel.app) and wired in through DEFAULT_API in docs/js/data.js.
3. Bundled real Yahoo snapshots (docs/data/snapshots.json: NDX, SPX, SPY, QQQ, AAPL, MSFT, NVDA, TSLA, AMZN, GOOGL, META, refreshed with python scripts/snapshot.py) when no API is reachable.

Repo layout

src/pricer/   bsm.py  binomial.py  lsmc.py  surface.py  data.py  viz.py  checks.py  cli.py  server.py
tests/        31 tests: reference values, parity, Greeks vs finite differences, tree convergence, LSMC, surface recovery, any-ticker data layer
docs/         the website (GitHub Pages)   ·   scripts/snapshot.py, build_guide.py   ·   METHODOLOGY.md, GUIDE.md

For AI agents (Claude Code, Codex) and contributors: read AGENTS.md first. It has the rules, commands and a handoff log the agents use to talk to each other.

Educational project, not investment advice. Market data from Yahoo Finance via yfinance, which may be delayed or inaccurate.