Does the IRS prefer one DLOM model over the others?

No. The Section 409A regulations list discounts for lack of marketability as a factor a reasonable valuation considers, but they do not name a model. The IRS's 2009 DLOM job aid for its own valuation staff discusses option-based methods and cautions that they are sensitive to inputs. What matters is reasonable, supported inputs and a clear explanation of how the concluded discount was reached.

Why can the Longstaff model produce a discount above 100%?

Longstaff measures the most an investor with perfect market timing would pay to be able to sell at the highest price during the holding period. That value is expressed as a percentage of today's price and is not capped, so at high volatility and long holding periods it can exceed the share's value. A discount above 100% has no practical meaning, which is why Longstaff is mainly used as an upper bound.

Should the DLOM holding period match the term used in the OPM?

In most reports, yes. Both represent the expected time until common holders can turn their shares into cash, so a reviewer will expect them to agree or the report to explain why they differ. A two-year OPM term paired with a four-year DLOM holding period, with no explanation, is a common audit comment.

Do appraisers use the same volatility in the DLOM model and the OPM?

Often, because both come from the same guideline company set over a matching look-back period. Some appraisers adjust it, since the OPM uses the volatility of total equity while the DLOM applies to a common share, which can be more volatile. Either way, the report should state where the figure came from and why it was used.

Does a secondary sale of common stock change the DLOM?

It can. A tender offer or an active secondary market shows that common holders have at least some access to liquidity, which may support a shorter holding period or a lower discount. An isolated, small or non-arm's-length secondary sale usually carries less weight. The appraiser should explain how any secondary activity was considered.

DLOM Models Compared: Finnerty vs Chaffe vs Longstaff vs Ghaidarov

How this page fits with our DLOM guides: This is the decision layer. Our Finnerty DLOM model guide and our Chaffe DLOM model guide walk through each formula and a full worked example. This page does not repeat that math. It compares all four models at the same inputs and explains when each one is the right tool.

What is a DLOM model, and why are there several?

A DLOM model estimates how much less a share is worth because it cannot be sold freely. Put-option models measure this as the cost of a put that would give the holder the liquidity they lack. There are several because each makes a different assumption about what that missing liquidity would have been worth.

In a 409A, the allocation step produces a value per common share on a marketable basis. That value assumes the holder could sell today. Startup employees and founders cannot: there is no public market, transfers usually need company approval, and liquidity normally waits for an acquisition or IPO. The discount for lack of marketability bridges the gap between the marketable value and the value the holder actually has.

The put-option models share one idea. If you owned a freely traded share, you could sell it whenever you wanted. A holder of restricted stock gives up that right for the holding period. The value of the right given up can be approximated by the price of a put option. The models disagree about which put:

Chaffe prices a put that guarantees today's price at the end of the holding period.
Finnerty and Ghaidarov price a put that lets the holder sell at the average price over the holding period, reflecting an investor with no special ability to time the market.
Longstaff prices a put that lets the holder sell at the highest price reached during the holding period, which assumes perfect market timing.

Each model needs the same two core inputs: volatility and the holding period, the expected time to liquidity. Chaffe also uses a risk-free rate. Because the inputs are shared, comparing the models at identical inputs isolates the effect of the model itself.

The Four Put-Option DLOM Models at a Glance

The table below summarizes each model's mechanics, its behavior as volatility rises and the role it usually plays in a 409A report. Empirical studies are included as a fifth row because most reports test the model output against them.

DLOM models comparison: mechanics and typical 409A role
Model	What It Prices	Key Assumption	At High Volatility	Typical 409A Role
Chaffe (1993)	European protective put, strike at today's price	Holder is guaranteed today's value at the end of the period	Rises steadily; can exceed empirical ranges	Primary model or upper reference point
Finnerty (2002, revised 2012)	Average-strike (Asian) put	Holder could have sold at the average price, with no timing skill	Flattens; capped near 32%	Primary model or lower reference point
Ghaidarov (2009)	Average-strike (Asian) put, alternative formulation	Same economic idea as Finnerty, without the ceiling	Keeps rising, approaching Chaffe	Alternative to Finnerty at higher volatility
Longstaff (1995)	Lookback put on the period's maximum price	Holder would have sold at the peak (perfect timing)	Grows fast; can exceed 100%	Theoretical upper bound only
Empirical studies	Observed discounts on restricted and pre-IPO stock	Past transactions are comparable to the subject shares	Not an input; ranges are fixed by the data	Reasonableness check on model output

Same Inputs, Four Answers: A Side-by-Side DLOM Comparison

The clearest way to see how the models differ is to run them on identical inputs. The table shows each model's DLOM at three input sets that roughly match a later-stage company near an exit, a typical growth-stage company and an early-stage company with a long road to liquidity. Chaffe uses a 4.0% risk-free rate and no dividends throughout.

Illustrative DLOM by model at identical inputs
Inputs	Finnerty	Ghaidarov	Chaffe	Longstaff
40% volatility, 1-year holding period	9.1%	9.3%	13.7%	36.1%
60% volatility, 2-year holding period	18.2%	19.9%	27.9%	87.7%
80% volatility, 4-year holding period	28.5%	39.2%	46.2%	204.9%

Finnerty figures use the revised average-strike put formula Finnerty published in 2012. Simplified approximations of the average-strike put that appear in some calculators give somewhat different results, so check which version a report used before comparing numbers across reports.

Three patterns stand out:

The ordering is stable. At every input set, Finnerty is lowest, Ghaidarov is next, Chaffe is higher and Longstaff is far above the rest. That ordering follows directly from the puts being priced: an average-price put is worth less than a fixed-strike put, which is worth less than a put on the maximum price.
The spread widens with uncertainty. Near an exit, Finnerty and Chaffe are less than five points apart. For the early-stage input set, the gap is almost 18 points. Model choice matters most for exactly the companies where the inputs are least certain.
Longstaff is not a usable point estimate at startup volatilities. A discount above 100% would mean the restricted share is worth less than nothing. That is why it serves as a ceiling.

To put the spread in dollars: on a marketable common value of $2.00 per share at 60% volatility and two years, Finnerty gives a non-marketable value of about $1.64 and Chaffe gives about $1.44. That 20-cent difference flows straight into the option exercise price.

Chaffe: The Protective Put

David Chaffe's 1993 model treats the DLOM as the cost of a European put with a strike equal to today's marketable value and a term equal to the holding period. It is standard Black-Scholes, so any reviewer can reproduce it in a spreadsheet. Its weakness is that, at high volatility and long horizons, it can produce discounts above what restricted stock and pre-IPO studies support.

The full formula, an eight-step worked example and a volatility-by-holding-period sensitivity grid are in our Chaffe DLOM model guide.

Finnerty: The Average-Strike Put

John Finnerty's model, first circulated in 2002 and published in revised form in 2012, prices an average-strike put. It assumes a holder of marketable stock would not have sold at the perfect moment, only at a typical price over the period. That makes it more conservative than Chaffe. One feature matters for model selection: Finnerty's published formula approaches a ceiling of about 32% however high volatility or the holding period go. For a seed company with 90% volatility and five years to liquidity, Finnerty alone can understate the discount that market evidence suggests.

For the formula, inputs, a worked Series A example and typical ranges, see our Finnerty DLOM model guide.

Ghaidarov: The Average-Strike Put Without a Ceiling

In 2009, Stillian Ghaidarov published a critique of Finnerty's original formulation and derived an alternative average-strike put. The economic idea is the same: the holder loses the ability to sell at the average price over the holding period. The math differs in a way that matters at high volatility. With no dividend yield, the Ghaidarov DLOM is:

DLOM = 2 × N(v√T / 2) − 1

v²T = ln[2 × (e^σ²T − σ²T − 1)] − 2 × ln(σ²T)

Here σ is annual volatility, T is the holding period in years, and N() is the standard normal cumulative distribution function. At low volatility and short horizons, Ghaidarov and Finnerty give almost the same answer: 9.3% versus 9.1% in the first row of the table. As uncertainty grows, the gap widens. Ghaidarov has no ceiling, so it approaches the Chaffe result at very high volatility.

In practice, appraisers use the Ghaidarov DLOM when they want the average-strike framing but believe Finnerty's cap understates the discount for an early, highly volatile company. A reviewer will expect the report to cite which average-strike formula was used, because the two can be ten points apart.

Longstaff: The Lookback Upper Bound

Francis Longstaff's 1995 paper asked a different question: what is the most an investor could lose from being unable to sell? His answer assumes an investor with perfect market timing who, if the stock were marketable, would sell at the highest price reached during the holding period. The value of that right is a lookback put. With no dividends, the Longstaff DLOM as a fraction of today's value is:

DLOM = (2 + σ²T / 2) × N(σ√T / 2) + √(σ²T / 2π) × e^{−σ²T / 8} − 1

Because nobody times the market perfectly, Longstaff is an upper bound, not an estimate. That is how Longstaff himself framed it. At low volatility and short horizons, it can be a useful ceiling: 36% for the near-exit case in our table. At startup volatilities and multi-year horizons, the result climbs past 100% and stops being informative.

A 409A report that concludes on a Longstaff DLOM alone, without explanation, is likely to draw questions. A report that shows Longstaff as an upper bound, with the concluded discount well inside it, is using the model as intended.

Finnerty vs Chaffe DLOM: which gives the higher discount?

Chaffe almost always gives the higher discount. At the same volatility and holding period, a fixed-strike protective put is worth more than an average-strike put, so the Chaffe DLOM exceeds the Finnerty DLOM. The gap is a few points near an exit and can exceed 15 points for early-stage companies with long holding periods.

The Finnerty vs Chaffe DLOM question is really a question about assumptions. Chaffe assumes the holder of a marketable share would have locked in today's value. Finnerty assumes they would have sold at a typical price along the way. Neither is wrong; they bracket a reasonable range.

That is why many appraisers run both. A concluded discount that sits between Finnerty and Chaffe, and inside the range of empirical studies, is easier to defend than a single-model number. When the two are far apart, the report should explain which end of the range the facts point toward. The Chaffe guide's section on choosing Chaffe over Finnerty covers the situations where each is the better primary model.

How do you choose a DLOM model for a 409A?

Choose a DLOM model by matching its assumptions to the company's stage, volatility and time to liquidity, then test the result against empirical evidence. Most appraisers run two or more put models, use Longstaff only as a ceiling, and conclude on a supported figure within the resulting range rather than on one model's output.

A practical approach to how to choose a DLOM model follows four steps:

Pin down the inputs first. Volatility should come from a supported guideline company set; our guide to Black-Scholes volatility inputs for a 409A covers how. The holding period should match the expected time to liquidity used elsewhere in the report, usually the option pricing model term.
Match the model to the stage. Near an exit, with moderate volatility, the models converge and the choice matters less. Chaffe or Finnerty alone may be enough. For early-stage companies with high volatility and long horizons, Finnerty's ceiling becomes binding, so pairing it with Chaffe or Ghaidarov gives a more complete picture.
Bracket, then conclude. Use the lower average-strike result and the higher protective put result as a range. Use Longstaff, where it is below 100%, as an outer limit. Conclude on a figure supported by the company's facts: a pending financing or active secondary market points lower, a long or uncertain path to exit points higher.
Test against empirical data. Compare the conclusion with restricted stock and pre-IPO study ranges for similar holding periods. A model result outside those ranges needs a stated reason.

Consistency also matters. Switching models between reports without a change in facts, especially when the switch lowers the exercise price, is the kind of choice that draws scrutiny. If the model changes, the report should say why.

Late-stage reports raise one more wrinkle. In a hybrid OPM/PWERM allocation, each scenario can carry its own DLOM: a short holding period for a near-term IPO and a longer one for the stay-private case. The model choice should be the same across scenarios unless there is a reason for it to differ.

Where Restricted Stock and Pre-IPO Studies Fit

Put-option models are theoretical. Empirical studies are the reality check. Two families are commonly cited in 409A reports:

Restricted stock studies compare the price of restricted shares of public companies with their freely traded price. Because SEC Rule 144 holding periods have been shortened over time, more recent studies tend to show lower discounts than older ones, and they reflect holding periods far shorter than a typical startup's.
Pre-IPO studies compare private transactions before an IPO with the later IPO price. They tend to show larger discounts, but critics note they also capture the risk that the IPO might not happen and the company's growth between the transaction and the offering, not just illiquidity.

Neither family maps neatly to a startup with a three- to five-year horizon. That is why they work best as a check on model output rather than a replacement for it. An appraiser who concludes a 35% discount for an early-stage company, between Finnerty and Chaffe and within the range of long-horizon empirical evidence, has three independent lines of support.

What Auditors and the IRS Look for in a DLOM

Treasury Regulations Section 1.409A-1(b)(5)(iv)(B)(1) lists the factors a reasonable valuation method considers, including control premiums or discounts for lack of marketability. The regulations do not prescribe a DLOM model. The AICPA's guide on valuing privately held company equity securities issued as compensation discusses put-option approaches, including protective put, average-strike and lookback models, without mandating one. The IRS's 2009 DLOM job aid for its valuation professionals discusses the same models and cautions against applying them mechanically.

In practice, reviewers look for:

Named models and formula versions. Which model was used, and for Finnerty or Ghaidarov, which formulation.
Supported inputs. A volatility source and a holding period consistent with the OPM or PWERM in the same report.
A range, not just a point. Results from more than one model, or a clear reason one model was enough.
An empirical cross-check. How the conclusion compares with restricted stock and pre-IPO evidence.
Consistency over time. The same approach across successive reports unless the facts changed.

Model choice alone does not create or remove safe harbor protection. A valuation by a qualified independent appraiser, as of a date no more than 12 months before the grant, is presumed reasonable under Section 1.409A-1(b)(5)(iv)(B)(2)(i), and the IRS can rebut that presumption only by showing the valuation is grossly unreasonable. An unsupported discount weakens that defense. If options are granted below fair market value and no exemption applies, they can become deferred compensation subject to Section 409A. If they then fail to comply, the holder may owe income tax on vested amounts, an additional 20% tax and interest. Our 409A safe harbor guide and our guide to audit-defensible 409A valuations cover the documentation that holds up.

The Bottom Line on DLOM Models Compared

The four put-option models are not competing answers to the same question. They are answers to slightly different questions about what liquidity is worth. Finnerty and Ghaidarov assume an ordinary seller, Chaffe assumes a locked-in price, and Longstaff assumes a perfect one. Seen that way, this DLOM models comparison is less about picking a winner than about building a defensible range.

When you read your 409A report, check which models were run, whether the inputs match the rest of the report, and where the concluded discount sits relative to each model and the empirical evidence. If only one model appears, ask why. For the mechanics of the two most common models, start with the Finnerty DLOM model and the Chaffe DLOM model, and for where the DLOM fits in the full report, see our overview of 409A valuation methodology.

The figures in this article are illustrative, computed from the published formulas with simplified inputs, and are not a valuation of any company. This article is general information about Section 409A and valuation practice, not legal, tax or accounting advice. Whether a valuation qualifies for a presumption of reasonableness under Treasury Regulations Section 1.409A-1(b)(5)(iv)(B) depends on the specific facts; consult your own counsel and tax advisor.