AbbottModelDLOM presents three exchange-option model families—Asian Average, Margrabe, and Longstaff—to evaluate the economic effect of restricted or delayed liquidity under different realization and information settings.
Each model combines market-based volatility with a supported period of restricted or delayed liquidity. The resulting exchange ratio is then converted to a discount measured relative to unrestricted value.
No single model is presumed to be appropriate for every assignment. Model selection should reflect the information available to market participants, expected realization process, characteristics of the subject interest, and purpose of the valuation.
Common Model Inputs
The models use two principal inputs:
- Daily volatility, represented by σ; and
- The applicable horizon in trading days, represented by T.
AbbottModelDLOM estimates daily volatility from continuously compounded logarithmic returns observed during the trailing 365 calendar days, corresponding to the conventional 252-trading-day year.
For DLOM analysis, the applicable horizon is:
TDLOM = Trestriction + Tblock
where:
- Trestriction is the legal or contractual restriction period, expressed in trading days; and
- Tblock is the estimated post-restriction block liquidation period, expressed in trading days.
A standalone blockage analysis uses only Tblock because it measures the period required to liquidate the block after disposition becomes legally permissible.
Consistent Time Scaling
Daily volatility is paired with a horizon measured in trading days. The same calculation can be expressed using annualized volatility and a horizon measured in trading years:
σdaily² × Tdays = σannual² × Tyears
where:
σannual = σdaily × √252
and:
Tyears = Tdays / 252
This scaling ensures that daily volatility is not paired incorrectly with a horizon expressed in years or annualized twice.
Common Equation Terms
The three models use the following common terms:
x = σ²T
z = √x = σ√T
where:
- σ is daily volatility;
- T is the applicable horizon in trading days;
- x is cumulative variance over the applicable horizon;
- z is volatility scaled to the applicable horizon;
- Φ(·) is the cumulative standard normal distribution function;
- R is the model-implied exchange ratio; and
- D is the resulting DLOM.
The equations presented below have been reconciled to the formulas used in the production model calculations.
Converting an Exchange Ratio to a DLOM
An exchange-option model measures the value of exchanging a restricted or less marketable interest for an otherwise equivalent unrestricted interest.
The resulting option premium or exchange ratio is not automatically the DLOM expressed as a percentage of unrestricted value.
For each model, AbbottModelDLOM converts the exchange ratio to a DLOM as follows:
DLOM = (R − 1) / R
Equivalently:
DLOM = 1 − (1 / R)
This conversion is important because treating an option premium measured relative to the restricted interest as the DLOM can overstate the discount, particularly when volatility or the model horizon is high.
Asian Average Model
The Asian Average model evaluates liquidity using an average realization price over the applicable horizon rather than assuming realization at one specific point in time.
The production calculation first defines:
A = x + ln[2(exp(x) − x − 1)] − 2ln[exp(x) − 1]
The Asian Average exchange ratio is:
RAsian = 2Φ(√A / 2)
The corresponding DLOM is:
DAsian = (RAsian − 1) / RAsian
Averaging reduces the effect of isolated price movements and generally produces a lower indication than models that assign greater value to timing flexibility or information advantages.
Within the AbbottModelDLOM framework, the Asian Average model represents a setting in which relevant public and private information has been credibly shared and neither party retains a material informational advantage.
This setting may be supported when effective due diligence has substantially reduced private-information asymmetry and the expected realization process is consistent with progressive or average-price liquidation.
The Asian Average indication should not be selected simply because it is the lowest result. Its use should be supported by the information environment and expected realization process applicable to the assignment.
Margrabe Model
The Margrabe model measures the value of exchanging a restricted or less marketable version of an interest for an otherwise equivalent unrestricted version.
The production Margrabe exchange ratio is:
RMargrabe = 2Φ(z / 2)
The corresponding DLOM is:
DMargrabe = (RMargrabe − 1) / RMargrabe
Because z = σ√T, the Margrabe indication responds directly to both return volatility and the supported period of restricted or delayed liquidity.
The securities used to develop AbbottModelDLOM’s reference-cohort evidence are publicly traded. Relevant public information and observable market pricing are therefore generally available to market participants. The Margrabe public-information condition is consequently the expected analytical starting point.
Material private information may nevertheless remain with the issuer, seller, management, or another informed party. The Margrabe model therefore provides the principal baseline when public-market information is available but complete private-information symmetry has not been established.
Longstaff Model
The Longstaff model uses a lookback-option structure that assigns greater value to the ability to select a favorable realization point during the applicable horizon.
The production Longstaff exchange ratio is:
RLongstaff = (2 + x/2)Φ(z/2) + √(7x/44) × exp(−x/8)
The corresponding DLOM is:
DLongstaff = (RLongstaff − 1) / RLongstaff
The lookback structure generally produces a higher indication than the Asian Average or Margrabe models because it assigns greater value to timing flexibility over the applicable horizon.
Within the AbbottModelDLOM framework, Longstaff provides a higher analytical benchmark when information asymmetry, realization uncertainty, or timing disadvantage is especially important.
The Longstaff result should not be treated as an automatic maximum DLOM or selected solely because it is the highest model output. Its relevance depends on whether the assignment facts support the model’s stronger timing and uncertainty assumptions.
Longstaff does not enter the costly-due-diligence progression described below. That decision framework focuses specifically on movement from the expected Margrabe public-information baseline toward the more information-symmetric Asian Average setting.
Information Settings and Model Selection
The three models provide a structured framework for considering different economic and information settings:
- Margrabe: the expected starting condition for publicly traded market evidence, with shared public information but possible continuing private-information differences;
- Asian Average: a possible post-due-diligence condition in which relevant public and private information has been shared and the realization process supports an average-price interpretation; and
- Longstaff: a higher lookback-based benchmark reflecting greater uncertainty, timing value, or information disadvantage.
These settings are analytical interpretations rather than automatic classifications.
Due diligence, access to management, financial-reporting quality, ownership concentration, transaction structure, investor availability, expected buyer behavior, and the anticipated method of realization may all affect the appropriate model interpretation.
Model selection should follow the economic facts of the assignment rather than a preference for a higher or lower discount.
Due Diligence as a Model-Selection Consideration
Due diligence can affect the information setting that supports model selection. It is not a separate DLOM adjustment and should not be added to, or subtracted from, a model indication.
Because the underlying reference and PIPE securities are publicly traded, the Margrabe public-information condition is the expected analytical baseline. The remaining question is whether material private information continues to be held by the issuer, seller, management, or another informed party.
Credible due diligence may allow that information to be evaluated and shared, reducing private-information asymmetry between the parties. If the resulting information environment becomes sufficiently complete and symmetric, the Asian Average interpretation may receive greater support.
The difference between the Margrabe and Asian Average indications can therefore be interpreted as the potential economic value of moving from the expected public-information baseline toward a more complete and symmetric information environment.
The maximum model-implied benefit of that progression is:
B = V₀ × max(DMargrabe − DAsian, 0)
where:
- B is the potential economic benefit of successful information production;
- V₀ is the pre-discount value of the subject interest;
- DMargrabe is the Margrabe DLOM; and
- DAsian is the Asian Average DLOM.
If p represents the probability that due diligence will successfully produce credible, decision-useful information and CDD represents the cost of that effort, due diligence may be economically rational when:
p × B > CDD
This condition is a model-selection aid. It helps the analyst evaluate whether the expected benefit of reducing private-information asymmetry may justify the cost of producing and verifying additional information.
The Margrabe–Asian Average spread is not an additional discount, information premium, or separately additive valuation adjustment. It should not be added to either model indication or deducted mechanically from a DLOM conclusion.
Completing due diligence also does not automatically justify selecting the Asian Average model. The analyst must evaluate the information state actually achieved. If credible due diligence substantially reduces relevant private-information differences and supports an average-price realization process, the Asian Average interpretation may receive greater support. If material private-information asymmetry remains, the Margrabe interpretation continues to provide the relevant baseline.
The calculated break-even amount is an upper bound on the potential value of successful information production. It is not an estimate of actual due-diligence expenditure or a guarantee that the corresponding pricing transition will occur.
Reference-Cohort Sensitivity Matrices
AbbottModelDLOM uses the lower-quartile, median, and upper-quartile volatility and liquidity evidence of the selected public-company reference cohort to develop sensitivity matrices for each model.
The matrices show how the model indication changes across supported combinations of volatility and liquidation-period evidence. They also allow the analyst to determine whether a conclusion remains stable across the cohort distribution or is particularly sensitive to one assumption.
For DLOM analysis, the matrices incorporate the applicable restriction period and post-restriction block liquidation period. For standalone blockage analysis, the matrices use only Tblock.
A sensitivity matrix is not a mechanical selection rule. The analyst must determine which combination of model, volatility, and horizon is most relevant to the subject interest.
Avoiding Double Counting
Volatility, liquidity, and the applicable horizon enter the exchange-option calculation as connected model inputs. They should not be converted into separate premiums and added again after the model result has been calculated.
A separate liquidity premium should not be added when the same liquidity evidence has already been used to determine Tblock. Similarly, Tblock should not be applied as an additional blockage adjustment when that same period has already been incorporated into the DLOM horizon, unless the analysis clearly separates and reconciles the two effects.
The Margrabe–Asian Average spread should likewise not be applied as an additional information-asymmetry adjustment. It is a model-selection aid that compares alternative information settings, not a separate component of DLOM.
Each economic constraint should be recognized once and in the appropriate part of the analysis.
Interpretation and Professional Judgment
The model indications are estimates derived from market evidence and stated assumptions. They are not observed transaction prices, guaranteed liquidation outcomes, or substitutes for assignment-specific analysis.
The analyst remains responsible for evaluating:
- the characteristics of the subject interest;
- the reliability and relevance of the selected reference cohort;
- the applicable restriction and liquidation periods;
- the information available to market participants;
- the results of any due-diligence process;
- the expected realization process; and
- the relevance of each model’s assumptions.
AbbottModelDLOM provides a transparent and reproducible framework for developing and comparing DLOM indications. It supports, but does not replace, professional judgment.