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Valuing Options with an EBITDA-Linked Strike in an Incomplete Market

Article Quant Q&A · Author: gmarais
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Summary

The document raises a valuation problem involving a derivative whose underlying share price is modeled with geometric Brownian motion while its strike changes with company EBITDA. The author questions whether the absence of a traded EBITDA instrument prevents construction of a replicating portfolio, making the market incomplete and a unique risk-neutral price unavailable. They also ask what valuation approaches might be appropriate when accounting rules require a value.

The document provides no answers or worked analysis, so it does not establish whether the proposed instrument is truly unhedgeable or specify an accounting method. It serves as a framing of the issue: a payoff can depend on both traded and nontraded risk, and the usual replication argument may not determine a unique price. Any practical conclusion would require details about the payoff, available hedges, assumptions for EBITDA behavior, and applicable valuation requirements.

Key ideas

  • The payoff depends on a share price and a strike linked to company EBITDA.
  • A nontraded EBITDA risk may limit replication using traded assets.
  • Market incompleteness can prevent replication from determining a unique derivative price.
  • The document poses accounting valuation questions but supplies no proposed method or answer.

Tags

OptionsDerivatives pricingRisk management
Full text
# Discounted payoff where S is risk-neutral and K is real-world


# Discounted payoff where S is risk-neutral and K is real-world












We are busy pricing a derivative (I think!) where the stock price is assumed to follow the usual GBM process. The strike however is not constant and follows a company's EBITDA.

Our theory is that: There is no market for a company's EBITDA and therefore we cannot setup a replicating portfolio. Something along the lines of an incomplete market (I am more than fuzzy on all the technical theory).

At the risk of being scolded I have two questions:

- Is this theory correct and does this mean that we cannot obtain a "risk-neutral" option price?

- If we are forced (by accounting requirements) to "value" this thing, what options (pardon the pun) do we have?

Hopefully a storm in a tea cup.

TLDR; I work for "one of the big four" audti firms and the departments are playing hot potato with this valuation. We have previously valued these instruments in the normal risk-neutral fashion but we have a new kid on the block who looked at this and asked the question.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.