The Chaffe DLOM Model, Explained: Protective Put Formula for 409A Valuations

Short answer: the Chaffe model says a share you cannot sell is worth less than an identical share you can sell by exactly the cost of insuring it against falling below today's price over the illiquidity period. Price that insurance with Black-Scholes, divide by the share value, and you have the Chaffe DLOM. It is simple, transparent and easy to reproduce, which is its main strength. It also tends to run high at the volatilities typical of startups, which is its main weakness.

This page is deliberately single-method. If you want the broader context on why DLOM exists at all and how the average-strike alternative works, start with our deep dive on the Finnerty DLOM model, which is the method most venture-backed 409A reports lead with. Here we stay focused on Chaffe.

What is the Chaffe DLOM model?

The Chaffe DLOM model is a put-option method for estimating the discount for lack of marketability. It treats illiquidity as the cost of buying an at-the-money European put that lets the holder sell at today's value when liquidity arrives. The put price divided by the share value is the DLOM percentage applied to non-marketable common stock.

David B. H. Chaffe III introduced the approach in “Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations,” published in Business Valuation Review in December 1993. At the time, most appraisers supported DLOM almost entirely with restricted stock studies, which compare the price of letter stock that could not be traded for a period with the freely traded shares of the same company. Chaffe's contribution was to show that a standard option pricing formula could produce discounts in a broadly similar range, while tying the result to observable, company-specific inputs rather than to averages from unrelated transactions.

In a 409A valuation, the Chaffe model sits near the end of the process. The appraiser estimates equity value, allocates it across preferred and common stock, usually with an option pricing model, and arrives at a marketable value per common share. The Chaffe DLOM then converts that figure into the non-marketable fair market value that supports option strike prices.

The Protective Put Intuition Behind Chaffe

Picture two investors holding the same common share worth $2.00 today. The first can sell at any time on a public exchange. The second holds startup common stock that cannot be sold until an acquisition or IPO, which the appraiser expects in about two years. The second investor bears a risk the first does not: if the company's value falls during those two years, there is no way to get out first.

Now suppose the second investor could buy a put option giving the right to sell the share for $2.00 at the end of the two years. That protective put restores much of what the liquid investor has — protection from being locked into a falling position. Chaffe's argument is that the price of that put is a reasonable proxy for the value lost to illiquidity:

• Protective put DLOM logic: marketable value − cost of the put ≈ value of the non-marketable share.
• Why at the money: the strike equals today's value, because the question is what it costs to lock in the current price.
• Why European: the holder can only use the protection when liquidity arrives, at the end of the holding period, not at any time before it.

The intuition is clean, and it explains why the model is still taught and used three decades later. It is also where the main criticism comes from, which we return to below: a protective put insures against price declines, but it does not literally make a share sellable, and it keeps all of the upside. A put and marketability are related, not identical.

The Chaffe DLOM Model Formula

The Chaffe DLOM model formula is the Black-Scholes-Merton price of a European put, expressed as a percentage of the share value. With the strike K set equal to the current value S:

Because S equals K, the ln(S/K) term drops to zero, and because startup common stock almost never pays dividends, q is normally zero as well. The formula then simplifies to a function of just three inputs:

N(·) is the cumulative standard normal distribution — NORM.S.DIST(x, TRUE) in Excel or Google Sheets. Because the result is a percentage, the share price itself never enters the simplified formula. One useful property follows directly: an at-the-money put can never be worth more than the present value of its strike, so the Chaffe DLOM is always below e^−rT, and therefore below 100%. That is not true of every put-based method; the Longstaff lookback approach, for example, can produce discounts above 100% at high volatilities.

Chaffe Model Inputs: Volatility, Holding Period and Risk-Free Rate

The Chaffe formula is only as defensible as its inputs. Each one should be sourced, dated and consistent with the rest of the 409A report.

Volatility (σ)

Volatility is the most influential input. Private companies have no trading history, so appraisers use the historical equity volatility of guideline public companies, measured over a lookback window roughly matching the expected holding period, and adjust for size, stage and leverage where they can support it. Early-stage startups commonly land in the 50% to 90% range. Critically, the volatility in the Chaffe calculation should match the volatility used in the OPM allocation, or the report should explain why it differs. Our guide to Black-Scholes volatility inputs for 409A covers peer selection and lookback choices in detail.

Holding period (T)

T is the expected time until a liquidity event, in years — not the time until the next financing round, which does not usually give common holders liquidity. It should match the term used in the OPM. Typical figures run from one year for a company in a signed acquisition or active IPO process, to three to five years for a seed or Series A company with no exit in sight.

Risk-free rate (r)

The risk-free rate is the yield on a US Treasury with a maturity matching T, as of the valuation date. It has a modest effect: a higher rate slightly lowers the Chaffe DLOM, because it raises the forward value of the stock relative to a fixed strike.

Dividend yield (q)

Almost always zero for venture-backed common stock. If a company does pay dividends, including the yield increases the put value and therefore the discount.

How do you calculate DLOM using the Chaffe model?

To calculate DLOM using the Chaffe model, set the strike equal to the current share value, choose volatility, holding period and risk-free rate, price an at-the-money European put with Black-Scholes, and divide the put price by the share value. The resulting percentage is applied to the marketable per-share value of common stock.

Here is a worked example for a Series A software company. The OPM allocation produced a marketable common value of $2.00 per share. The appraiser expects a liquidity event in about two years, the guideline public company volatility is 60%, and the two-year Treasury yield on the valuation date is 4.0%.

On these inputs the Chaffe model indicates a discount of about 27.9%, taking the common stock from $2.00 to roughly $1.44 per share before the appraiser weighs it against any other DLOM indications. The spreadsheet version is a single line: =EXP(-r*T)*NORM.S.DIST(-d2,TRUE)-NORM.S.DIST(-d1,TRUE). For how the DLOM step fits into the full chain from enterprise value to strike price, see our end-to-end 409A valuation example.

Chaffe DLOM Sensitivity: Volatility vs Holding Period

Because the Chaffe model has so few inputs, its behavior is easy to map. The table below shows the Chaffe DLOM at a 4.0% risk-free rate and zero dividend yield across the volatility and holding-period combinations most often seen in startup 409A work.

Two patterns stand out. First, the discount is close to linear in volatility over this range: every additional 20 points of volatility adds roughly 7 to 12 points of DLOM. Second, the holding period matters most in the first couple of years and then flattens. That is why a well-supported volatility estimate does more for the defensibility of a Chaffe result than fine-tuning T. It is also why the bottom-right corner of the table — discounts above 45% — should prompt a hard look at whether the inputs, not the model, are driving the answer.

When Do Appraisers Choose Chaffe Over Finnerty?

For the same volatility and holding period, a European put is worth more than the average-strike put Finnerty uses, so the Chaffe model almost always returns the higher discount. Applying the same 70% volatility and three-year horizon used in our Finnerty DLOM walkthrough, the Chaffe DLOM comes out at about 37.5% with a 4.0% risk-free rate — roughly ten points higher than the Finnerty result on that page. We will not repeat the Finnerty mechanics here; the practical question is when that gap justifies using Chaffe.

• As a reasonableness check. The most common role. Running Chaffe next to Finnerty brackets the reasonable range, and a concluded DLOM that sits between the two is easier to explain than a single-model figure.
• At lower volatilities and shorter horizons. When a later-stage company has 40% to 50% volatility and one to two years to a likely exit, the gap between the models narrows and Chaffe's transparency is an advantage.
• When the downside is the real risk. If the holder's main exposure is being locked in through a decline — a company facing a difficult financing environment, for example — the protective put framing matches the economics well.
• For audit-ready simplicity. Chaffe can be reproduced by a reviewer in one spreadsheet cell with standard functions. Some auditors and reviewers value that more than theoretical refinement.

Chaffe is generally a weaker choice as the sole method for high-volatility seed-stage companies with long horizons, where it can produce discounts well above what restricted stock studies and pre-IPO studies support. In that setting most appraisers weight Finnerty, empirical data, or both more heavily. How the DLOM methods are combined is one of the judgment calls covered in our overview of 409A valuation methodology.

Is the Chaffe model accepted for 409A valuations?

Yes. The Chaffe model is a recognized put-option DLOM method, discussed in the AICPA's valuation guide for privately held company equity securities and in the IRS DLOM job aid for its own valuation professionals. Neither mandates it; acceptance depends on reasonable, well-supported inputs and a documented rationale for how the result is used.

The regulatory hook is Treasury Regulations Section 1.409A-1(b)(5)(iv)(B)(1), which lists the factors a reasonable valuation method considers, including “control premiums or discounts for lack of marketability.” The regulations do not prescribe any specific DLOM model. What they require is that the overall method be reasonable and consistently applied.

Model choice alone does not create or remove safe harbor protection. The independent appraisal presumption under Section 1.409A-1(b)(5)(iv)(B)(2)(i) applies when a qualified independent appraiser prepares the valuation as of a date no more than 12 months before the grant; the IRS can then challenge the value only by showing it is grossly unreasonable. A Chaffe discount built on stale volatility or a holding period inconsistent with the rest of the report is exactly the kind of weakness that invites that challenge. Our 409A safe harbor guide explains the presumptions and how they can be lost.

The IRS DLOM job aid is worth knowing about because it signals how an examiner may think. It acknowledges option-based methods, including the protective put, but cautions that they are sensitive to volatility and holding-period assumptions and should not be applied mechanically. Reviewers want to see the inputs justified and the result tested against other evidence.

Limitations and Common Criticisms of the Chaffe Model

• A put is not marketability. A protective put guards against a decline in value but does not let the holder sell, rebalance or use the shares as collateral. Critics argue the model therefore measures price insurance, not the full cost of illiquidity — and that because the holder keeps all the upside, the analogy is imperfect.
• It runs high at startup volatilities. As the sensitivity table shows, volatility above 80% combined with holding periods of three years or more pushes the discount past 40%. That can exceed what empirical evidence supports.
• It ignores the path. A European put only cares about the value at the end of the holding period. Finnerty's average-strike put and Longstaff's lookback put each respond to this in different ways, producing lower and higher bounds respectively.
• Input consistency is easy to break. Using one volatility for the OPM and another for the DLOM, or a holding period that ignores a live acquisition process, produces results that do not reconcile — a frequent reviewer comment.
• No company-specific liquidity factors. Transfer restrictions, rights of first refusal, the likelihood of company-run tender offers and secondary market access all affect marketability but do not appear in the formula. Appraisers address them qualitatively.

How to Review the Chaffe DLOM in Your 409A Report

Founders and CFOs do not need to rebuild the model, but they should be able to check it. When a 409A report cites the Chaffe DLOM model, look for these points:

1. Inputs are stated. Volatility, holding period, risk-free rate and dividend yield should each appear with a source and the valuation date.
2. Inputs match the OPM. The volatility and term should be the same as those used to allocate value to common stock, or the difference should be explained.
3. The holding period fits your facts. If you are in an acquisition process or preparing an IPO, a four-year horizon is hard to defend. If you are pre-revenue with no exit in view, a one-year horizon is equally suspect.
4. There is a cross-check. The report should compare the Chaffe result with Finnerty and ideally with empirical data, then explain how the concluded DLOM was selected.
5. The discount moves sensibly over time. Across successive 409As, DLOM should generally fall as the company matures and the expected liquidity date approaches. A rising discount without a clear reason deserves a question.

These are the same issues auditors raise when they review stock-based compensation under ASC 718. Our guide to audit-defensible 409A valuations covers what else reviewers test once the report is in their hands.

The Bottom Line on the Chaffe DLOM Model

The Chaffe DLOM model is the most intuitive of the quantitative marketability methods: the cost of a protective put, priced with Black-Scholes and divided by share value. It is easy to reproduce, easy to audit and firmly established in valuation practice. Its weakness is that it tends to produce larger discounts than other methods at the high volatilities and long horizons typical of early-stage startups. Used as one indication alongside Finnerty and empirical evidence, with inputs that match the rest of the report, the Chaffe model makes a 409A valuation more defensible, not less.

This article is general educational information about valuation methodology and IRC Section 409A. It is not tax, legal or accounting advice. Consult a qualified valuation professional and tax advisor about your company's specific facts.