Two Approaches to Valuing Equity Options with Share Dilution

Summary

The document raises a valuation question about European options or warrants that dilute existing shareholders. It outlines two proposed adjustments: scaling a Black–Scholes value by the inverse of one plus a dilution ratio, or first adjusting the share price for the shares and options issued, then recalculating the option value using Black–Scholes.

It provides no answer, derivation, numerical example, or evidence comparing the approaches, so it does not establish which method is appropriate. The central issue is how newly issued shares and the option’s value affect the underlying equity value and per-share payoff. Any analysis would need to specify the corporate action, share counts, and option terms; the document alone is insufficient to resolve the question.

Key ideas

• The document presents two proposed ways to adjust a Black–Scholes option value for dilution.
• One proposal scales the option value using a dilution ratio.
• The other recalculates the option using an adjusted share price that accounts for issued shares and options.
• No derivation or conclusion is provided to show which approach is correct.

Tags

# Black Scholes with Dilution


# Black Scholes with Dilution












I've seen two ways to account for dilution when valuing a European option using Black Scholes. I'm not sure which is the correct way and why these methods differ. The two ways I've seen are:

1) Multiplying the value of the warrant/option by 1/(1+q) where q is the amount of dilution (e.g. q is the number of options over basic shares plus options)

2) Using an adjusted share price to calculate d1, d2 and the value of the call. This adjusted share price is calculated the number of shares outstanding multiplied by the share price plus the value of the call option (as calculated by Black-Scholes) multiplied by the number of options being issued. This is then divided by the number of options being issued plus the basic shares outstanding, which gives you an adjusted diluted share price, which you then run Black-Scholes with to get the value of the diluted call option.

Can you please advise which (if any) of these methodologies are correct?

Many thanks!

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