amanlig/covered-call-exit-model

Covered-call exit scenario model

Compare closing a covered-call position now with waiting to close or rolling the call now and closing the resulting position later. The model estimates USD cash flows and whole-position profit, and ranks replacement calls under explicit strike, expiry and quote-quality criteria.

The core combines two methods:

1. Historical return bootstrap: generates possible future stock-price paths.
2. Black–Scholes European call formula: estimates the option liability at a future exit, using a constant implied volatility calibrated for each contract.

This is an experimental mathematical scenario engine, implemented in Python's standard library. It has no neural-network weights, training pipeline, broker connection or order execution. Downloading the repository does not create a hosted inference API. The included data is entirely synthetic.

Simulation at a glance — aiMoney dashboard chart

This image is rendered by aiMoney's actual React dashboard chart component, using the included synthetic model inputs. It is the same chart used in the app, with all three rollover controls shown in Close mode. The screenshot is static; its Close/Expire controls and hover details are interactive only in aiMoney.

The example holds 100 shares covering one $40-strike call, with a captured stock midpoint of $50, a stock purchase cost of $3,005 including fees, and $800 recorded net option cash including prior linked cycles. Everything is fictional.

Each strategy has three adjacent columns:

Chart element	Meaning
Green Sale, with any blue segment above	Stock sale/assignment proceeds, plus replacement premium where applicable
Red Buyback	Call-buyback cost, drawn upward as a cost magnitude; subtract it from sale cash
Purple P/L	Estimated whole-position profit, including recorded option cash and original stock cost/fees
Brown horizontal line	Original stock purchase cost before purchase fees
Net P/L label	The strategy's total profit, matching the purple bar
Exit cash label	Sale cash less buyback costs; it excludes historical cash/basis adjustments
Sale-floor and funding labels	Simulated floor-pass fractions and estimated net cash needed to roll

Close today is the fixed captured-bid/ask reference: $1,575.03 total profit. The other groups are the model's three highest-ranked replacement calls. Their cash-flow bars and P/L summarize the same 600 simulated stock paths, with a 30-trading-day review horizon. Earlier expirations settle within each path. The costs and proceeds shown for future exits are discounted mean amounts.

How the model produces this chart: three months of artificial historical returns → 600 bootstrapped stock paths → Black–Scholes values for unexpired replacement calls → stock/option exit cash flows and expiry settlement → 4% discounting → recorded cash/basis adjustments → rank by estimated profit.

The purple bar is the whole-position result; a tall red buyback bar by itself is not an overall position loss. The figure shows Close-mode comparisons only. Switching to Expire in aiMoney shows conditional option-only cash while retaining shares, which is a different valuation basis. This chart does not draw percentile whiskers; simulation ranges are available in the reference JSON.

The original dashboard component and styles render this image directly; the plot values are not redrawn by a separate plotting library. Every purple bar is checked against examples/expected_result.json. Provenance records the frontend source checksums. To regenerate from an aiMoney frontend checkout, install the optional playwright dependency and Chromium, then run:

python3 examples/render_aimoney_chart.py --frontend-dir /path/to/aiMoney/frontend

The model itself remains standard-library only. These sample results illustrate its arithmetic and assumptions; they do not establish that a rollover will outperform closing in actual markets.

Run the example

Requires Python 3.10+; no pip installation or credentials are needed. From the downloaded repository:

python3 run_example.py
python3 -m unittest discover -s tests

The example writes example_result.json and example_rollovers.csv (Excel-compatible, UTF-8 with BOM). CSV contains every matching rollover, ranked by total position profit descending. These outputs demonstrate code behavior, not investment performance.

Python usage:

import json
from model import evaluate, call_price

with open('examples/sample_input.json') as stream:
    inputs = json.load(stream)

result = evaluate(inputs, horizon=30, paths=600, seed=42, rate=0.04)
for choice in result['top_choices']:
    print(choice['expiry'], choice['strike'], choice['total_pl_usd'])

# Fictional standalone pricing example: 23 days to expiry, 80% annual IV.
print(call_price(spot=50, strike=52, years=23/365,
                 volatility=0.80, rate=0.04))

To evaluate supplied data or change the assumed interest rate:

python3 run_example.py --input my_inputs.json --rate 0.041

rate is a continuously compounded annual USD rate expressed as a decimal. The default 4% is a fixed assumption, not an automatically retrieved market yield.

Mathematics

1. Stock-price paths: historical bootstrap

From completed daily stock closes in the preceding three calendar months:

$$r_t=\ln (P_t\mathrm{/}{P}_{t-1})r\_t=\backslash ln(P\_t/P\_\{t-1\})$$

Each simulated day independently samples one historical log return with replacement, then updates price:

$$S_{j+1}=S_j\exp (r_j^{\ast })S\_\{j+1\}=S\_j\backslash exp(r\_j^*)$$

Every path starts at the captured stock bid/ask midpoint (or the selected hypothetical stock midpoint). Default settings are 600 paths, 30 trading days, and random seed 42. All strategies face the same paths. At least 40 unique completed closes are required. The model retains the historical sample's drift rather than imposing risk-neutral drift on stock paths.

The option IV is not the stock-path volatility input: the paths use historical returns directly. They are generated independently of the Black–Scholes formula.

2. Option prices: Black–Scholes, without dividends

For remaining time $T>0$:

$$C=S\mathrm{\Phi }(d_1)-K{e}^{-rT}\mathrm{\Phi }(d_2)C=S\backslash Phi(d\_1)-Ke^\{-rT\}\backslash Phi(d\_2)$$

$$d_1=\frac{\ln (S\mathrm{/}K)+(r+{\sigma }^2\mathrm{/}2)T}{\sigma \sqrt{T}},d_2=d_1-\sigma \sqrt{T}d\_1=\backslash frac\{\backslash ln(S/K)+(r+\backslash sigma^2/2)T\}\{\backslash sigma\backslash sqrt\{T\}\},\; \backslash qquad\; d\_2=d\_1-\backslash sigma\backslash sqrt\{T\}$$

Symbol	Meaning
$C$	European call value in USD per share
$S$	Stock price in USD per share
$K$	Strike in USD per share
$T$	Remaining calendar time in years, using 365 days
$r$	Continuously compounded annual risk-free-rate assumption
$\sigma$	Annual implied volatility as a decimal, e.g. 0.80 = 80%
$\Phi$	Standard normal cumulative distribution function

At expiry the call's intrinsic value is $\max(S-K,0)$.

Reference: Durham University mathematical finance notes, section 5.4. The implementation uses math.erf to evaluate the normal CDF.

3. Calibrate implied volatility to the captured midpoint

For each usable option, solve:

$$C(S,K,T,\sigma ,r)=(\mathrm{b}\mathrm{i}\mathrm{d}+\mathrm{a}\mathrm{s}\mathrm{k})\mathrm{/}2C(S,K,T,\backslash sigma,r)=(\backslash mathrm\{bid\}+\backslash mathrm\{ask\})/2$$

implied_volatility() uses 70 binary-search iterations over annual volatility 0.0001 to 8.0. The contract is excluded if its midpoint fails the implemented Black–Scholes price-bound check. The search has no explicit final convergence check for prices requiring IV beyond its bounded search interval.

This version calibrates IV itself; it does not directly use a broker's reported IV field. Matching the original midpoint is calibration, not independent proof of pricing accuracy. Captured IV stays constant for subsequent scenario pricing.

4. Estimated liquidation and expiration

At a future exit before expiry, estimate the buyback ask as:

$${\mathrm{a}\mathrm{s}\mathrm{k}}_{future}=C(S_{future},K,T_{remaining},\sigma ,r)+({\mathrm{a}\mathrm{s}\mathrm{k}}_{captured}-{\mathrm{b}\mathrm{i}\mathrm{d}}_{captured})\mathrm{/}2\backslash mathrm\{ask\}\_\{future\}=C(S\_\{future\},K,T\_\{remaining\},\backslash sigma,r)\; +(\backslash mathrm\{ask\}\_\{captured\}-\backslash mathrm\{bid\}\_\{captured\})/2$$

Use stock bid for stock sales, the held call's captured ask to close it now, and the replacement's captured bid to sell it now. Future stock bids use the captured stock half-spread, floored at zero.

When replacement expiry occurs on/before the exit horizon, the model settles it at an approximate expiry step: $\max(1,\lceil\mathrm{calendarDays}\times252/365\rceil)$. At/above strike the short call is assigned and covered shares deliver at strike; otherwise the call expires and retained shares sell at the review horizon. Assignment cash earns the assumed rate until review. Calendar-to-trading-day conversion is approximate; there is no holiday calendar or intraday expiry model. Early assignment is not modeled.

5. Cash flows, discounting and whole-position profit

For a rollover the model counts the held-call buyback and replacement premium once, then includes the stock and replacement liability at the selected exit. Future cash is discounted with $\exp(-r,d/252)$ for $d$ trading days. Immediate rollover cash is not discounted as though it occurred at the future horizon.

$$\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{P}\mathrm{L}=\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{L}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}+\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{C}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{H}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{O}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}-\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{P}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{I}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{d}\mathrm{F}\mathrm{e}\mathrm{e}\mathrm{s}+\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{k}\mathrm{e}\mathrm{d}\mathrm{P}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{r}\mathrm{C}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{O}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{P}\mathrm{L}\backslash mathrm\{totalPL\}=\backslash mathrm\{discountedLiquidationCash\}\; +\backslash mathrm\{currentCycleHistoricalOptionNetCash\}\; -\backslash mathrm\{stockPurchaseCostIncludingRecordedFees\}\; +\backslash mathrm\{linkedPriorCycleOptionPL\}$$

The caller supplies recorded history; the engine does not reconstruct a trade ledger. Fees included in supplied history/cost must already be allocated once. Future execution fees and taxes are excluded.

net_profit_usd is current-cycle whole-position P/L; total_pl_usd also adds linked prior-cycle option P/L. Missing required accounting inputs leave profit unavailable, not zero. Partial known earlier receipts may remain visible.

Rows report simulated mean, 10th/90th percentiles, sale-floor pass fraction and fraction beating immediate close. mean, p10, and p90 are discounted liquidation wealth, not historical-cost-adjusted P/L. Add the same recorded cash/basis adjustment to translate them into whole-position P/L.

Candidate criteria and ranking (version 1.13)

• Standard 100-share calls, with shares exactly covering the contract count.
• Replacement strike at least 1.20 times original USD purchase price and strictly above the current/scenario stock midpoint. No fixed upper strike cap.
• Expiry after valuation date, through one calendar year after held-call expiry. Same-day expiry and the exact held contract are excluded.
• Validated contract; finite positive noncrossed bid/ask; reported delay zero; not halted; both option bid/ask sizes at least the number of contracts.
• Implied-volatility calibration must pass the price-bound check described above.
• A sale floor of 1.10 times purchase price is reported with pass fractions. Floor failures and negative estimated profits remain eligible for display.

rows includes every matching rollover plus close/wait benchmarks. The engine sorts diagnostic rows by floor eligibility and mean wealth; top_choices selects the three highest net_profit_usd rollovers regardless of floor failure or profit sign. For one position with complete history, adding common prior-cycle cash does not change profit ordering. run_example.py explicitly sorts the full rollover CSV by total_pl_usd, with unavailable totals last.

The optional stock-price scenario helper reprices captured calls at a selected spot within ±50% of captured midpoint, retaining calibrated IV and absolute spreads, then re-evaluates. Applications should preserve the original captured close-today benchmark when displaying such hypothetical scenarios.

Conditional worthless-expiry outcome

Each rollover also has expire_worthless: assume its replacement expires worthless, without assignment, with all shares retained. The existing held-call buyback is still paid now; the replacement needs no later buyback.

This outcome is option cash/P/L only. It excludes retained stock value and is not comparable whole-position profit. Even its total_pl_usd field is an option-only total including linked prior cycles. net_profit_usd is null in this outcome. This version requires an explicit future-stock valuation assumption to construct a comparable whole-position expiry result; none is silently added.

Synthetic sample data

examples/sample_input.json is fully fictional and regenerated with python3 examples/make_sample.py. It contains:

Field	Synthetic example
Symbol/account	DEMO / SYNTHETIC
Valuation date	October 28, 2026 (fixed; not the current date)
Position	100 shares covering 1 call
Original stock purchase	$30/share plus $5 recorded purchase fees
Captured stock bid/ask	$49.95 / $50.05
Held call	$40 strike, January 15, 2027 expiry
Synthetic call quotes	Generated from Black–Scholes at 65% IV, midpoint ±$0.10
Current-cycle historical option net cash	$700
Linked prior-cycle option P/L	$100
Current-cycle completed-call P/L	$200 (component; do not add again)
Replacement candidates	Three matching contracts, one below-spot rejection, one delayed-quote rejection

History is an artificial sequence generated with seed 17 and a fixed menu of returns. Weekday labels omit weekends but do not model exchange holidays. Quote sizes and validation flags are synthetic examples, not live verification.

On the provided fixture, the default run produces approximately:

Strategy	Estimated whole-position P/L, USD
Close now	1,575.03
Roll to March 19, 2027, strike $60	2,258.35
Roll to December 18, 2026, strike $55	2,234.84
Roll to November 20, 2026, strike $52	2,049.97

These values only verify a reproducible example. The sample does not establish forecast accuracy, an expected investment return or a winning strategy.

Validation and limitations

The repository includes 16 synthetic unit tests covering reproducibility, constraints, accounting, expiry outcomes, funding and scenarios. These are software correctness checks. There is no historical option-chain backtest, out-of-sample forecast evaluation, or validated prediction-accuracy metric.

The model assumes independent historical-return samples, constant calibrated IV, constant captured spreads and a fixed review horizon. Short history restricts tail scenarios and ignores volatility clustering. European pricing approximates American equity calls; dividends, early assignment, corporate actions, taxes, future fees, cash/margin limits, changing liquidity and alternative reinvestment opportunities are omitted. Quote validation uses supplied flags/sizes and does not independently verify quote timestamps or guarantee fills. Zero reported delay alone cannot prove that a saved quote is recent.

Use it to explore explicit assumptions and audit arithmetic. It is not an execution system or a validated investment recommendation engine.

Files and provenance

• model.py: unchanged standalone aiMoney model, version 1.13.
• run_example.py: JSON evaluation and full ranked rollover CSV export.
• examples/sample_input.json: synthetic fixture.
• examples/make_sample.py: deterministic fixture generator.
• examples/expected_result.json: complete reference output for the fixture.
• examples/expected_rollovers.csv: matching ranked reference export.
• tests/test_model.py: synthetic unit tests.
• examples/simulation-profit.png: annotated bar chart of the synthetic simulation.
• examples/render_aimoney_chart.py: optional capture script using the original aiMoney frontend and Playwright.
• examples/simulation-chart-provenance.json: chart and input/output checksums.
• manifest.json: SHA-256 checksums of the package payload.

The package contains no real portfolio records, brokerage credentials, private captures, transaction confirmations, screenshots or account identifiers. It makes no network requests during evaluation. A caller must supply and validate its own market data and respect the data provider's redistribution terms.