Covered Call Backtester

A from-scratch Python backtester for the covered call overlay strategy. Prices options with Black-Scholes (using math.erf for high-precision CDF), estimates IV from rolling historical volatility with regime-based multipliers, and simulates day-by-day trade decisions over multi-year price histories.

Quick start

# 1. Set up the environment (one time)
python3 -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

# 2. (Optional) Download fresh price data — there's already an MSFT CSV in the repo
python download_prices.py                   # default: MSFT, 10y
python download_prices.py --ticker AAPL     # any ticker
python download_prices.py --ticker SPY --period 5y

# 3. Run the backtest
python cc_backtest.py

Sample output (MSFT 2016-04 → 2026-04, $100K portfolio):

Capital:                         $  100,000.00
Contracts (100 shares each):               20    ($95,573.55 stock + $4,426.45 cash)

Returns
    Buy & Hold Final:            $  746,166.44     +646.17%
  + Net Overlay P&L:             $  268,424.87     +268.42 pp
  = CC Overlay Final:            $1,014,591.31     +914.59%

Overlay P&L Breakdown
    Gross Premium Collected:     $  998,518.91    (income from 181 calls sold)
  - Buybacks + Assignment Costs: $  730,094.04    (paid to close ITM calls + capped upside on assignment)
  = Net Overlay P&L:             $  268,424.87    (26.9% retained)

Activity
    Calls Sold:                            181
    Win Rate:                             81.1%
    Max Drawdown:                        22.86%

Statistical Significance (H0: overlay adds zero value vs. buy-and-hold)
    Days in Sample:                      2514    (9.98 years)
    Annualized Excess Return:          +1.249%
    Annualized Excess Vol:               9.90%
    Sharpe of Excess Return:           +0.126
    t-stat (naive, IID):                +0.40    (assumes independence — inflated for overlays)
    t-stat (Newey-West, L=8 ):          +0.46    (correct: accounts for position autocorrelation)
    Clears t=2 bar?                     False    (conventional significance)
    Clears t=3 bar (HLZ 2016)?          False    (multiple-testing adjusted)

Degrees of Freedom — 3-year in-sample window (Pardo 2008)
    Observations (trading days):          756
    Consumed (3 params + 30 LB):           33
    Remaining (free):                     723    (95.6% — Pardo floor 90%)
    Bar-level DOF adequate?              True    (necessary, not sufficient)
    Independent trades (median):           36    (grid range 17-73)
    >= 30 trades for inference?          True    (clears it; 2-year window would not)

The portfolio is sized into whole 100-share contracts at the initial price; any leftover (here, $4,426 of $100K with MSFT at ~$48) sits as 0%-yield cash. Returns are measured against capital, so the cash drag is included. To run a single-contract simulation, omit capital from params.

The bottom block tests whether the overlay's excess return over buy-and-hold is statistically distinguishable from zero, using Newey-West HAC standard errors that correct for the autocorrelation introduced by holding the same option position across multiple days. On this MSFT sample the t-stat is 0.46 — well below the conventional significance bar of 2 — meaning the $268K of headline overlay P&L isn't reliably distinguishable from noise. See the tutorial's Part 5 for the full reasoning.

The final block reports Robert Pardo's degrees-of-freedom check for the default 3-year walk-forward training window. Both checks pass: the bar-level test (756 observations minus 3 free parameters and a 30-bar indicator lookback leaves 95.6% free, above Pardo's ~90% floor) and — the binding one — the ~30-trade sample-size floor, which the 3-year window clears (median 36 trades). The window is sized to 3 years precisely for that: a 2-year window leaves the median grid fit at ~24 trades, short of the floor. Note this is necessary, not sufficient — a clean DOF check means the model isn't over-parameterized, not that the edge is real (the t-stat above settles that). See tutorial Part 4.

For an explanation of each output line — including what "assignment loss" means and why buybacks can dominate the overlay's gross premium income — see the tutorial (its Glossary defines the terms; Part 3 walks through the trade-by-trade math).

Tests

pytest test_cc_backtest.py          # run the full test suite
pytest test_cc_backtest.py -v       # verbose
pytest --cov=. --cov-branch         # with coverage

CI runs ruff, pyright, the test suite, and a backtest smoke test on every PR — see .github/workflows/ci.yml.

Project layout

File	What it is
cc_backtest.py	Backtest engine: Black-Scholes pricing, rolling vol, regime-based IV, day-by-day overlay state machine, Newey-West t-stat reporting on excess returns
test_cc_backtest.py	Unit and scenario tests covering pricing, the overlay state machine, and the statistics helper
download_prices.py	yfinance data downloader
make_figures.py	Regenerates the tutorial and blog figures (fig1–fig13) into docs/figures/
make_notebook.py	Regenerates the runnable notebook from the tutorial markdown + figure script
msft_10yr_prices.csv	Sample MSFT price data, 2016-04 to 2026-04
tutorial_covered_call_backtest.md	Long-form tutorial — theory, math, code walkthrough, and statistical-significance testing
covered_call_backtest.ipynb	Runnable notebook companion to the tutorial — open in Colab via the badge above, or generate locally with python make_notebook.py
docs/figures/	Generated PNGs embedded in the tutorial; regenerable from make_figures.py
requirements.txt	Runtime + dev dependencies

Where to start: the tutorial is the source of truth for why every part works the way it does (Black-Scholes math, rolling vol, the overlay state machine, walk-forward optimization, robustness checks). For what a function actually does, read cc_backtest.py end-to-end — it's heavily commented and the link jumps to run_cc_overlay, the engine entry point. For the behavior the engine guarantees, see the scenario tests in test_cc_backtest.py covering the major trade flows: sell + expire OTM, called away, profit-target close, and multi-cycle accumulation.

Strategy parameters

Edit the params dict at the bottom of cc_backtest.py:

Param	Default	Meaning
call_delta	0.25	Target delta for strike selection (≈25% chance ITM at expiry)
close_at_pct	0.75	Close when 75% of premium has been captured
dte	21	Days to expiration when opening a new call
risk_free_rate	0.045	Annual risk-free rate used in Black-Scholes
capital	cost of 1 contract	Total dollars committed; sized into whole 100-share contracts (leftover sits as 0%-yield cash)

IV is no longer a tunable param — it's derived from rolling 30-day historical vol times a regime-based multiplier (1.1× / 1.3× / 1.5× for high / normal / low vol).

Caveats

This is an educational backtester, not a production trading system. Notable limitations:

• IV is estimated, not real (no historical option chain data).
• No earnings-week avoidance, no dividend handling, no rolling logic.
• Single-stock, single-period results — see the tutorial's robustness section for how to evaluate generalizability.