Financial Reporting
Black-Scholes Inputs for Private Companies: Where Volatility, Term, and Rate Come From
Your 409A sets the stock price input. Here's how private companies derive the other four ASC 718 assumptions: volatility, expected term, rate, and dividends.
By 409.AI Team - 2026-08-28
# Black-Scholes Inputs for Private Companies: Where Volatility, Term, and Rate Come From
An auditor pulls up your stock comp schedule and asks a simple question: where did the 55% volatility number come from? If the honest answer is "our valuation firm typed it in," you have a problem. ASC 718 doesn't just require that you run an option-pricing model. It requires that every input into that model be defensible on its own, and for a private company, four of the five inputs don't come from anywhere on your cap table.
Most founders already know their 409A fair market value feeds the stock price input in Black-Scholes, the model [ASC 718 uses to turn a stock option into a compensation expense](https://409.ai/articles/asc-718-stock-based-compensation-startup-guide). What's less understood is where the other four numbers, expected volatility, expected term, the risk-free rate, and expected dividends, come from when your company has no public trading history to pull them from. Here's how each one gets built, and why the shortcuts exist for a reason.
The problem with a private company and a public-company model
Black-Scholes was built for stocks that trade every day. A private company's shares don't trade at all, which means three of its five inputs (volatility, expected term, and to a lesser extent the risk-free rate) have no direct source. You can't look up your own historical volatility because there's no price history to measure. You can't observe how long employees really hold their options because you may not have years of exercise data yet. The model still needs numbers, so accounting standards and SEC guidance built specific, sanctioned ways to estimate them without inventing anything.
Expected volatility: borrow it, on purpose
Volatility measures how much your stock price is expected to swing over the life of the option, expressed as an annualized standard deviation. It's the single input option value is most sensitive to: higher volatility means a wider range of possible upside, and because an option's downside is capped at zero while its upside isn't, more volatility mechanically means a more valuable option.
A private company has no trading history to calculate this from directly. The SEC's [Staff Accounting Bulletin Topic 14](https://www.sec.gov/interps/account/sabcodet14.htm) addresses this gap directly: when a newly public or nonpublic entity lacks sufficient company-specific historical or implied volatility, it's appropriate to base the estimate on the historical, expected, or implied volatility of comparable public companies, sometimes called guideline companies. The idea is straightforward. If you're a Series C SaaS company, you look at the historical volatility of publicly traded SaaS companies of similar size, growth rate, and stage, then use that as a proxy for your own.
This is a judgment call, not a formula. Which companies count as comparable, how much weight to give each one, and what measurement window to use all move the number. That's why most companies bring in a third-party valuation firm rather than picking a peer set themselves: an appraiser who does this across hundreds of private companies has a defensible, repeatable process, and can document it the way an auditor expects. It's the same discipline behind the guideline-company work in an [OPM allocation](https://409.ai/articles/409a-allocation-methods-opm-pwerm-backsolve), which is itself built on the Black-Scholes framework, just solving for equity value instead of option value.
Expected term: the simplified method, and its limits
Expected term is how long, on average, an option is expected to stay outstanding before it's exercised or expires. Estimating this properly requires years of your own exercise data: how long employees typically wait after vesting, how often they exercise early, how attrition affects the pattern. Almost no private company has that history yet.
The SEC's [Staff Accounting Bulletin No. 107](https://www.sec.gov/rules-regulations/staff-guidance/staff-accounting-bulletins/staff-accounting-bulletin-no-107) created a "simplified method" for this situation: for plain-vanilla options (standard vesting, no unusual features), expected term is estimated as the midpoint between the vesting period and the contractual term. A grant that vests over four years with a ten-year contractual life gets an expected term of (4 + 10) / 2, or seven years. SAB 107 was originally set to expire at the end of 2007; the SEC's follow-up bulletin, [SAB 110](https://www.sec.gov/oca/staff-accounting-bulletin-110), removed that sunset date because the industry-wide exercise-behavior data the SEC expected to become available still hadn't materialized. The simplified method remains available today, but only when a company doesn't have enough of its own historical exercise data to support a more refined estimate, and only for options without unusual features like reload rights or performance conditions.
That last condition matters more than it looks. If you extend a post-termination exercise window well past the standard 90 days, or grant options with vesting tied to a performance milestone instead of time, you may no longer qualify for the simplified method, and your expected term (along with your option value) can move meaningfully. We've covered how [extending the exercise window changes the underlying valuation math](https://409.ai/articles/extending-post-termination-exercise-window-iso-nso-409a) in more depth.
Risk-free rate: matching the clock, not just the market
The risk-free rate is the least judgment-heavy of the four, but it's also the most commonly gotten wrong by companies who plug in whatever Treasury yield is topical that week. ASC 718 ties the rate to the yield, on the measurement date, of a zero-coupon instrument (Treasury STRIPS are the standard reference) with a remaining term matching the option's expected term, not its contractual term.
That means the expected-term estimate has to be settled first. A grant with a seven-year expected term uses something close to the seven-year Treasury STRIPS yield on the grant date, not the ten-year yield tied to the contractual life of the option. If the expected term falls between two available maturities, say six years when quoted maturities are five and seven, standard practice interpolates a rate between them. It's a small input in dollar terms compared to volatility, but auditors check it because it's the easiest one to verify against public data, and it's an easy place to catch a company that copy-pasted last year's assumption sheet.
Expected dividends: usually zero, but say why
For nearly every venture-backed startup, expected dividend yield is zero. The assumption should reflect a company's historical dividend policy adjusted for what management expects going forward, and most private companies that are reinvesting everything into growth have no dividend history and no near-term plan to start one. If your company has paid dividends before, or has a stated policy, that changes the number. A higher dividend yield lowers option value, since a shareholder who exercises early and holds the stock benefits from dividends that an option holder doesn't get until exercise.
The reason this input still shows up in a valuation memo, even at zero, is documentation. An auditor wants to see that dividend yield was a conscious assumption tied to your actual dividend history and expectations, not a default nobody looked at.
When Black-Scholes stops being the right tool
Black-Scholes assumes a single expected term and constant volatility for the life of the option, which works well for a standard four-year vest with a ten-year contractual term and no unusual features. It starts to break down for awards with features Black-Scholes can't represent: reload provisions, performance-based vesting, expected changes in volatility or exercise behavior over time, or contractual terms long enough that early-exercise patterns matter. FASB's implementation guidance under ASC 718 doesn't require a specific model, but it does note that a lattice, or binomial, model can incorporate assumptions that vary over an option's life and can more accurately reflect substantive exercise behavior that a single-point Black-Scholes calculation can't capture. For most early-stage grants, Black-Scholes with well-documented inputs is enough. It's worth flagging to your valuation provider if your plan includes reload features, market-condition vesting, or unusually long contractual terms, since those are the situations where the model choice itself starts to matter as much as the inputs.
Getting it audit-ready
None of these four inputs are supposed to be arbitrary, and none of them are supposed to come from the company itself. Volatility comes from a defensible peer set, the same discipline the [AICPA's guidance on valuing private-company equity](https://409.ai/articles/aicpa-cheap-stock-guide-2026-update-409a-valuation) applies to the stock price input. Expected term comes from either your own exercise history or a documented, rules-based simplified method. The risk-free rate comes from a specific Treasury instrument matched to that same expected term. Dividend yield comes from your actual history and policy. Put together, they turn an option grant with no market price into a defensible expense number, the same way your [409A valuation](https://409.ai/articles/what-is-a-409a-valuation-a-comprehensive-guide) turns illiquid common stock into a defensible fair market value.
The practical move is to treat the assumption set as part of the valuation deliverable, not an afterthought your accounting team fills in separately. A valuation memo that documents the peer companies used for volatility, the method behind the expected term, the specific Treasury yield applied, and the reasoning for the dividend assumption is what satisfies an auditor asking where the numbers came from. If your current [ASC 718 stock comp process](https://409.ai/products/asc-718) treats these four inputs as boilerplate rather than documented judgment calls, that's usually the first thing to fix before your next audit, not after it flags something.