# Methodology — How OptionsAhoy Calculators Compute Results | OptionsAhoy > Show-your-work page for the OptionsAhoy free calculators: tax bracket sources, AMT computation, Black-Scholes assumptions, return defaults, and known scope gaps. Markdown twin of https://optionsahoy.com/methodology (canonical). More for agents: https://optionsahoy.com/llms.txt Methodology # How the calculators compute results For five-figure-and-up equity decisions, you should know what's going on under the hood. Below is the math, the data sources, and the things we deliberately don't model in the free tools. ## Tax computation Federal ordinary income. Marginal walk across the 2026 IRS brackets (single, married-filing-jointly, head-of-household) published in IRS Rev. Proc. 2025-32. Income added by an exercise or vest is walked from the user's stated baseline through the brackets it crosses. Federal long-term capital gains. 0% / 15% / 20% brackets per filing status, plus the 3.8% Net Investment Income Tax (NIIT) above the MAGI threshold ($200K single, $250K MFJ). State income + LTCG tax. Per-state ordinary brackets for 2025 (most states publish 2026 brackets in late 2026). Long-term capital gains follow ordinary brackets in most states; preferential treatment modeled for HI, ND, SC, WI, AR, NM. Washington's 7% LTCG-only tax above $270K modeled separately. Payroll taxes (FICA). When still employed: 6.2% Social Security up to the 2026 wage base ($184,500), 1.45% Medicare on all wages, plus 0.9% Additional Medicare on wages above $200K (single) / $250K (MFJ). Source verification. Every 2026 federal constant above — ordinary brackets, long-term capital gains breakpoints, the AMT exemption and phaseout, and the FICA wage base — is asserted against its IRS Rev. Proc. 2025-32 published value by an automated conformance test. A stale or mistyped figure fails the build before it can ship. ## AMT computation Alternative Minimum Tax follows IRC §55: AMTI = ordinary income + ISO bargain element. Federal: 26% up to $244,500 of AMTI (post-exemption), 28% above. Exemption ($90,100 single / $140,200 MFJ for 2026, per IRS Rev. Proc. 2025-32) phases out at 50¢ per $1 of AMTI above the threshold ($500,000 single / $1,000,000 MFJ; the post-OBBBA rate applies as of 2026 per IRC §55(d)(4)). State AMT modeled for the four states currently in the registry: CA, CO, CT, and MN. CT piggybacks on federal AMT (lesser of 19% of federal TMT or 5.5% of federal AMTI); CA, CO, and MN apply flat rates above a state-specific exemption. Other states: state TMT treated as zero. The AMT-ISO calculator's optimizer searches for the share count and timing that maximizes net final value (after a qualifying disposition) net of AMT premium. Federal AMT credit recovery is modeled when regular federal tax exceeds federal tentative minimum tax in a future year. Cash return rate. The optimizer time-values the cash-tax stream at a user-set rate (default 5%, roughly the short-Treasury yield). At rate = 0 the math collapses to a nominal-sum objective; above zero, early AMT premiums get penalized against spread schedules and late credit recoveries get discounted. ## Volatility and option pricing Put and call premiums use closed-form Black-Scholes with the underlying's implied volatility. When a tracked options chain is available, σ is read directly from the chain, interpolated to the user's strike (set by their protection level) and tenor. When no chain is available (bare tools page, pre-IPO companies, untracked public tickers), the protective put tool falls back to a sector-typical realized volatility (e.g. 36% Tech Software, 45% Semiconductors). The concentration tool's hedge math uses the same sector vol scaled by 1.20 to approximate the implied-over-realized premium typical for buying single-name puts, since concentration does not pull chain data directly. This fallback is approximate by design; real quotes vary with skew, tenor, and strike. Each tool surfaces the σ value it used so you can sanity-check before committing. ## Return assumptions Single-stock expected return. When a public ticker is selected, the slider seeds from a blend of trailing-window CAGRs (2-year chain history, 5-year, 10-year where available, anchored at a 5-year mid-horizon for the wind-down calculators). On the bare page (no ticker selected) and for pre-IPO companies, the default is 20%/yr. The slider exposes the full range so users with stronger or weaker views can adjust. Diversified market return. SPY's trailing return seeds the slider, with a haircut applied for volatility drag (½ × variance × T). 10% is the unseeded default. Volatility drag (haircut). The expected-sale-price haircut maps from σ via the lognormal half-variance correction (1 − exp(−σ² × T / 2)), growing monotonically with the hold period. On chain-equipped public tickers it is seeded from the chain's at-the-money implied σ over the user's hold horizon; without a chain, it defaults to a 20% haircut. The same mapping powers the concentration tool's drag on the held concentrated position (diversified reinvestment is left unhaircut since it already represents a vol-averaged return). ## QSBS (IRC §1202) qualification The QSBS checker runs six statutory tests against the user's facts (entity type, acquisition method, asset category at issuance, industry, active-business posture, holding period, adjusted basis, expected gain) and returns a verdict, the applicable exclusion percentage, and the federal tax saved. The two Section 1202 conditions it does not test, non-corporate shareholder status and the redemption rules around issuance, are the user's to confirm. Four exclusion eras are covered: 50% (acquired 1993-2009), 75% (acquired 2009-2010), 100% (acquired 2010 through 2025-07-04), and the OBBBA tiered regime (50% / 75% / 100% at 3- / 4- / 5-year holds, with caps lifted to $15M / $20M for stock acquired on or after 2025-07-05). State conformity is tracked: non-conforming (CA, AL, PA, MS), partial (HI, MA), and NJ's 2026-01-01 conformity switch are all modeled. Pre-2010 acquisitions retain the 7% AMT preference on the excluded gain. ## What's NOT modeled in the free tools - Multi-scenario optimization. Each free tool projects one expected case. The full beta product runs bullish, neutral, and bearish in parallel and finds the schedule that performs best across all three. - Joint optimization across grants. Each tool models a single grant or position. Beta solves the multi-year exercise + vest + sale + hedge schedule across your whole equity portfolio. - Double-trigger RSUs. Most pre-IPO RSU grants don't settle until a liquidity event. The RSU calculator models single-trigger only. - $100K ISO limit (§422(d)). Annual ISO grants whose FMV at grant exceeds $100K are reclassified as NSO from the start. The free tool assumes you're within the limit. - Multi-state moves and dual residency. Single state per scenario; relocation timing not modeled. - Disqualifying dispositions. ISO projections assume a qualifying disposition (≥1 year from exercise, ≥2 years from grant). Early sales convert to NSO ordinary-income treatment — out of scope. - §83(b) elections. Out of scope. ## Trust and verification Every figure on this page traces to a citable source, and the engine behind the tools is built to be checked, not taken on faith. - Sourced to IRS authority. Brackets, Alternative Minimum Tax exemptions, and thresholds come from the 2026 IRS Revenue Procedures cited above; the QSBS checker runs six statutory Section 1202 tests. - Deterministic. The same inputs on the same date produce the same result (deadline and holding-period figures move with the calendar). No language model sits in the calculation path; the recommended schedule is produced by exact deterministic optimization and validated against brute-force results on a published tractable case. See the [verification page](https://optionsahoy.com/verification) for the math beside the IRS publications and an independent tax engine. - Private by design. No account, and the calculators compute in your browser: the numbers you enter are not transmitted to our servers, and we never sell or share them. If you ask us to email you a scenario, we keep that request as described in the [privacy policy](https://optionsahoy.com/privacy). - Open source. The calculation engine is public under the MIT license at [github.com/AlvisoOculus/optionsahoy-mcp](https://github.com/AlvisoOculus/optionsahoy-mcp). Audit it yourself. - Tested. More than a thousand automated tests cover the federal and 50-state tax logic, AMT credit recovery, and the option-pricing model. Estimates only. Not financial advice. [Back to free tools.](https://optionsahoy.com/tools)