Choosing the Stock Price for Valuing a Capital-Increase Right

Summary

The document asks which underlying share price should enter a Black–Scholes calculation used to value a preferential right issued during a capital increase. It gives prices for the issue date and the preceding day, notes that a dividend is paid on the issue date, and identifies an ex-dividend theoretical equilibrium price derived from the prior closing price. It also states the proposed relationship between the right’s value and a call option’s value, adjusted by a dilution factor.

The central practical issue is aligning the option’s underlying price with the valuation date and the dividend treatment. However, the text is only a question: it does not establish which of the candidate prices is correct, explain the rights’ terms, or provide a solution. A reliable valuation would require the relevant contract details and a consistent treatment of the dividend and capital increase; the document alone cannot resolve the input choice.

Key ideas

• The question concerns the underlying share-price input for Black–Scholes valuation of a preferential right.
• The stated relationship scales a call option value by a dilution adjustment.
• The issue date coincides with a dividend payment, making the ex-dividend price relevant to the pricing question.
• The document does not supply an answer or enough contract detail to select one of the candidate prices.

Tags

# Capital increase: which stock price to use as input to Black-Scholes formula?


# Capital increase: which stock price to use as input to Black-Scholes formula?












For an exercise we have to calculate the theoretical value of a scrip / preferential right on its issue day (23 April) in the context of a capital increase. The scrips are issued on 23 April. The closing price of the stock on that day is 4.70 euro, while the closing price of 22 April is 5.35. A dividend of 0.20 is paid on 23 April. The theoretical equilibrium price is 4.2833 based on the ex-dividend price of 22 April, 5.15 euro.

We have seen the following formula, to calculate the scrip price based on the price of a call option, which in turn we have to calculate through Black-Scholes:

$P(scrip)=(\frac{1}{1+q})*P(calloption)$ with q the dilution factor.

When calculating P(calloption) through Black-Scholes, which price do you use as the current stock price? 5.15? 4.2833? or 4.70?

(If this is not the right place to ask this question, please refer me to the right website)

Thank you in advance

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