How European option thinking shows up when valuation writers talk about a discount for lack of marketability — and why this site is not a DLOM calculator.
→ European BSM calculator (not a DLOM tool)This article is for valuation-curious students and self-taught readers. It is not valuation, legal, tax, accounting, or appraisal advice. Standards, case law, and agency practice change. Nothing here is a workpaper, a court exhibit, or a substitute for a credentialed professional and current primary sources.
blackscholes-calculator.com is not a DLOM calculator. It does not ship WACC models, restricted-stock databases, pre-IPO study tuners, 409A workpapers, ASC 718 engagement software, or a “marketability discount” button. The homepage prices European calls and puts under Black-Scholes-Merton. That is the entire quantitative product.
We still write this page because homework sets, CFA-style readings, and valuation textbooks keep colliding with options language. A student who has just learned a European put will meet Chaffe and think the calculator has secretly become an appraisal suite. It has not. The put is a framing some practitioners use when they talk about illiquidity. Framing is not a delivered tool.
If you need the algebra of the European put itself, use the Black-Scholes tutorial and the calculator. If you need volatility-as-an-inversion, use implied volatility. If you need the 1973 story, use history. Come back here only for the translation layer: why a put appears in a DLOM paragraph at all.
In business valuation, interests in private companies (and some restricted public shares) often cannot be sold as easily as a listed common share. Buyers of those interests bargain for a lower price. Appraisers give that bargain a name: discount for lack of marketability (DLOM). It is related to, and easy to confuse with, a discount for lack of control (DLOC). Control is about who directs the firm. Marketability is about who can exit, how fast, and at what friction.
Evidence people actually use in the wild falls into messy families:
A student should keep those families separate. An option number does not retire Mandelbaum. A restricted-stock average does not prove a European put is the “right” insurance. And none of those families is a WACC. Cost of capital and marketability discounts answer different questions; mixing them in one slider is how people invent software this site refuses to be.
David B. H. Chaffe III’s 1993 note is the classroom doorway. The story: if you hold an interest you cannot sell for a stated period, you are exposed to price moves you cannot exit. A European put on that interest, struck at today’s marketable value, would let you put the shares back at that price at the end of the restriction. The premium of that put, as a percent of the marketable value, is offered as a DLOM.
Why a put? Because the economic picture is insurance against a lower price at the date you are finally allowed to sell. Why European? Because the original Black-Scholes closed form — and Chaffe’s use of it — assumes you cannot exercise along the way. That matches this lab’s calculator and mismatches many real restrictions (you might sell earlier if a window opens; you might never get a clean expiry).
On the homepage calculator, set S and K equal, choose a T that looks like a restriction length, pick a σ, and read the put price. Divide by S if you want the Chaffe-shaped percentage. Then stop. You have illustrated an analogy. You have not valued a company, supported a tax filing, or computed a WACC.
Sensitivities follow the Greeks you already know. Longer T and higher σ raise the European put, so the Chaffe-shaped percentage rises. Rate (rho) matters more when T is several years — the same warning the Greeks page gives for long-dated options. Those comparative statics are useful for homework intuition. They are dangerous if you treat vega as a substitute for a volatility workpaper you do not have.
The homepage calculator will accept whatever σ you type. In a DLOM / put-style reading, that is the wrong lesson. Guideline public-company equity volatility is an observation about those companies’ residual claims. It is not yet the volatility of the subject firm’s assets, and it is not yet the volatility of the subject company’s equity at the subject company’s (firm’s) leverage. The usual teaching path — not a button on this site — looks like this.
Begin with an observed or estimated equity volatility for the guideline public companies (or, rarely, for the subject if it has a usable return history). That is typically the annualized standard deviation of log equity returns over a lookback that rhymes with the restriction or holding period. The implied-volatility guide covers peer selection and lookback; this page only insists that you name the object: equity vol of those names, still loaded with their capital structures.
Smaller and thinner names often show higher equity volatility than large, liquid comps in the same industry. If the guideline set is a mega-cap cohort and the subject is a small private interest, copying σ without a size thought is a category error. Size and trading-liquidity effects are a high-level overlay here — a reason the GPC σ may sit too low — not a second model we ship. Do not double-count: a size overlay on vol and a DLOM on the interest can tell the same economic story twice if you are careless.
Equity is the residual claim after debt. Higher financial leverage, all else equal, raises equity volatility even when the business is unchanged. To strip that effect, practitioners unlever guideline equity vol to an asset (firm) volatility — the volatility of the operations, as if the capital structure were all-equity. That asset vol is the bridge. Put-style DLOM thinking often wants this object, not the raw GPC equity σ, because the insurance picture is about the value of the firm (or the interest as a claim on the firm), not about a public peer’s particular D/E.
If the European put is conceptually on the subject’s equity, you still do not plug the GPC’s equity vol. You relever the asset vol at the subject company / firm leverage ratio so the amplification matches the subject’s debt and equity mix — not the guideline median’s. If the put is read against the firm (asset) value, you may stop at asset vol. Either way, leverage is how you travel between equity vol and asset vol; it is not optional decoration.
There is no size-slider, no unlever widget, and no “subject D/E” field on the homepage. You may still type a σ into the European calculator to see how the put moves. Choosing that σ — GPC equity vs asset vs subject equity after relever — is judgment this lab does not automate.
A protective put priced on raw guideline equity vol imports the comps’ leverage into the discount. Unlevering isolates business risk. Relevering, if you need it, happens at the subject company’s (firm’s) leverage, not the peer’s. Students who skip the bridge treat σ as a free parameter; practitioners who write files are supposed to be able to say which claim — assets or equity — the put is insuring.
Later writers argued that a plain European put overstates the “insurance” you need, because you do not actually want protection against every down move — you want compensation for not being able to time a sale. Average-price (Asian-style) puts associated with John Finnerty, lookback-style ideas associated with Francis Longstaff, and other adjustments (including work circulated under names such as Ghaidarov) try to change the payoff so the implied discount is smaller or differently timed.
You do not need the full paper trail to see the pedagogical point: once you leave a European vanilla put, you have left this website’s engine. Finnerty-style average strikes are not a toggle on the homepage. Lookbacks are not a toggle. We will not fake them with a second “DLOM mode.”
Closest to what you can see with this lab’s European put. Also the framing most often accused of overstating a discount.
Different contracts. Different numerics. Mentioned so you recognize names in a reading list — not so we pretend to compute them.
A student who only hears “Black-Scholes DLOM” will think there is one official number. There are several analogies, plus empirical and qualitative families. Naming the cousins is how we keep the European put from sounding like a statute.
A downloadable “DLOM%” with a logo, a claim that Chaffe is required, a broker referral, or a binary/event-contract aside. We will not add those. If you want a professional conclusion, you want an appraiser and a file — not a static HTML lab.
Worked path, if you are studying rather than filing:
The About page already says the site is not valuation SaaS. This guide exists so a DLOM keyword does not undo that sentence. We would rather rank for an honest explanation than for a tool we refuse to build.
The calculator is the 1973 European map: prices, Greeks, IV, payoff, parity. It is not a DLOM calculator and it does not ship WACC.
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