Risk-Neutral Valuation of Rights Issues and Share Dilution

Summary

The document considers how to value a corporate rights issue, in which existing shareholders receive rights to buy additional shares at a stated price. Although an individual right resembles a call option, the issue grants rights broadly to shareholders, so exercising them increases the share count and dilutes existing ownership. The question asks whether a modified Black-Scholes framework can capture this effect.

The response says that dilution treatments can be extended to rights issues, but emphasizes that the subscription price is often sufficiently low that exercise is expected, reducing the practical importance of modeling the option-like feature. It therefore directs attention toward the change between undiluted and fully diluted shares outstanding. This is a brief conceptual answer rather than a valuation derivation: it supplies no risk-neutral formula, assumptions, empirical examples, or method for quantifying dilution. The appropriate treatment may depend on the offer terms and whether exercise is genuinely close to certain.

Key ideas

• A rights issue gives existing shareholders an opportunity to buy additional shares at a stated price.
• Because rights are distributed to shareholders, exercising them increases shares outstanding and dilutes ownership.
• When the subscription price makes exercise highly likely, dilution may matter more than optionality.
• The document offers no risk-neutral pricing formula or quantitative dilution procedure.

Tags

# Risk-neutral models for rights issues


# Risk-neutral models for rights issues












A rights issue is the granting by a corporation to its shareholders of a right to purchase $N$ new shares for each $M$ shares they already hold at a (often discounted) price $K$. Thus, it superficially resembles a call option, but because every shareholder is holding such options, dilution of the stock value is unavoidable. Are there any papers out there which would contain a description of a risk-neutral valuation of rights issue, e.g. using a modified Black-Scholes model?

## Answer by Brian B (score 2)

https://quant.stackexchange.com/a/8878

I think Hull treats dilution in his book, and it's extensible to this case. For what it's worth, the strike is typically set low enough that there's little doubt about exercise, meaning there's not much point in modeling the optionality. Most people concentrate on the dilution alone -- particularly the question of the change in fully diluted versus undiluted shares outstanding.

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