What is the Finnerty model formula for DLOM?

The Finnerty (2012) model prices the DLOM as an average-strike Asian put: DLOM = e^(−qT) × [N(v√T ⁄ 2) − N(−v√T ⁄ 2)], where v√T = √( σ²T + ln[2(e^(σ²T) − σ²T − 1)] − 2·ln(e^(σ²T) − 1) ), σ is equity volatility, T is the restriction period in years, q is the dividend yield, and N(·) is the standard normal CDF.

What DLOM does the Finnerty model produce at 60% volatility and a 2-year term?

Approximately 18.2% with no dividends. At 40% volatility and 1 year it produces about 9.1%; at 80% volatility and 3 years about 26.3%. The model asymptotically caps near 32.6% regardless of inputs.

Why does the Finnerty model cap around 32.6%?

Because it prices an average-strike put — insurance at the average price over the restriction period rather than at the starting price. As volatility times term grows large, the value of that insurance converges to a mathematical limit of roughly 32.6% of the stock price, which keeps the model's output within the range observed in restricted stock studies.

Finnerty vs. Chaffe — which DLOM model should be used for a 409A?

Best practice is to compute both (plus restricted stock study benchmarks), understand why they differ, and document the concluded DLOM inside that range with a written rationale. Chaffe's protective put is generally the upper bound because it insures the full starting price while the holder keeps the upside; Finnerty's average-strike put is typically lower and better behaved at long terms and high volatility.

DLOM · Methodology

The Finnerty Model DLOM: Formula, Worked Example, and When Auditors Challenge It

FairValueX Team · 8 min read

Bottom Line: The Finnerty model prices the discount for lack of marketability as an average-strike put option on the restricted shares. At 60% volatility and a 2-year restriction period it produces a DLOM of about 18.2%, and it asymptotically caps near 32.6% — which is exactly why auditors like it and why it rarely supports very large discounts on its own.

What the Finnerty Model Is

In a 409A valuation, after equity value is allocated to common shares, the concluded value is reduced by a discount for lack of marketability — the price of not being able to sell. Option-based DLOM models make that price literal: they ask what an option that insures the holder against the inability to trade would cost.

Finnerty (2012) models that insurance as an average-strike (Asian) put: protection at the average price over the restriction period, not the price on day one. The logic: a restricted holder doesn't know when within the period they would have sold, so the model averages over the whole window rather than assuming perfect timing.

The Formula

                DLOM = e−qT × [ N( v√T ⁄ 2 ) − N( −v√T ⁄ 2 ) ]

                where  v√T = √( σ²T + ln[ 2( eσ²T − σ²T − 1 ) ] − 2·ln( eσ²T − 1 ) )

✓ σ — equity volatility (annualized), from the same peer-group analysis used elsewhere in the valuation
✓ T — expected restriction period in years (time to a liquidity event or expected holding period)
✓ q — dividend yield (typically 0 for venture-stage companies)
✓ N(·) — standard normal cumulative distribution function

The result is the put value expressed directly as a percentage of the marketable share value — the DLOM.

Worked Example: σ = 60%, T = 2 Years

Take a Series B company: peer-group volatility 60%, expected time to liquidity 2 years, no dividends.

σ²T = 0.36 × 2 = 0.72
e^0.72 = 2.0544, so e^σ²T − σ²T − 1 = 2.0544 − 0.72 − 1 = 0.3344
ln(2 × 0.3344) = ln(0.6688) = −0.4023
2·ln(e^σ²T − 1) = 2·ln(1.0544) = 0.1059
v²T = 0.72 − 0.4023 − 0.1059 = 0.2118, so v√T = 0.4602
N(0.4602 ⁄ 2) = N(0.2301) = 0.5910 and N(−0.2301) = 0.4090
DLOM = 0.5910 − 0.4090 = 18.2%

Sensitivity Table

Volatility (σ)	Term (T)	Finnerty DLOM
40%	1.0 yr	9.1%
50%	1.5 yr	13.6%
60%	2.0 yr	18.2%
70%	2.0 yr	20.7%
80%	3.0 yr	26.3%

Computed directly from the formula above with q = 0. Values are model outputs, not concluded discounts — the concluded DLOM is a documented judgment.

The 32.6% Ceiling — Feature, Not Bug

As σ√T grows, the Finnerty DLOM converges to a mathematical limit of roughly 32.6%. Auditors know this number. It keeps the model's output inside the range of observed restricted stock study discounts, which is precisely why the model reads as credible — and why a valuation that needs a 45% DLOM cannot get there with Finnerty alone. If your concluded discount exceeds the model output, the gap must be bridged with documented qualitative factors, not model shopping.

When Auditors Challenge the Finnerty Model

❌ Volatility inconsistent with the rest of the report

Using one volatility in the OPM allocation and a different one in the DLOM without reconciliation is the fastest way to draw a question.

❌ Term unsupported

T should tie to the same liquidity-event timing used in the allocation (OPM term or PWERM scenarios) — not chosen to move the discount.

❌ Single-model reliance

Best practice presents Finnerty alongside Chaffe and restricted-stock benchmarks, with the conclusion documented inside the range.

❌ No sensitivity analysis

Auditors want to see how the DLOM moves for reasonable input ranges — the table above is the shape of the exhibit they expect.

How FairValueX Documents DLOM

Every FairValueX binder computes Finnerty and Chaffe side by side from inputs already sourced elsewhere in the report, benchmarks the result against restricted stock studies, and records the concluded discount with an explicit judgment memo — the exact exhibit an auditor's valuation specialist asks for. See the DLOM deep dive for the full framework, or why DLOM is the #1 audit target in 409A review.

Related Resources

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