Zur Bewertung von Optionen und Optionsscheinen (Warrants)

Abstract

On the Valuation of Options and Warrants

This contribution deals with the problem of valuing options and emphasizes an aspect which has scarcely been given any consideration in the option pricing theory developed in recent years: the diversification effect of options within the overall framework of the investor’s portfolio. The theory of option pricing proceeds from a special hypothesis concerning the price trend of the shares for which options are concluded and investigates the functional interrelationship between the current share price and the option price. Since no endogenous determination of the share price is undertaken on the basis of equilibrium conditions, the diversifying effect of options within the investor’s portfolio is likewise disregarded. In contrast, the present study adopts the method of a more general equilibrium analysis. First of all, it is shown that the classical capital market model is unsuitable for dealing with options on account of its postulate that all investors demand the same portfolio; in contrast, the Fischer Black variant of the model, which knows no riskfree form of investment, proves a suitable instrument for dealing with our problems. Two results obtained by applying the valuation principles derived from this model to the problem of option pricing deserve special mention. - Generally speaking, there is no functional relation between current share price and option price, but only a relation between current share price and option price which is governed by the future (uncertian) trend of the share price within the framework of the market. - Even if special preconditions imply a functional relation between current share price and option price, such relation coincides with that obtained with option pricing theory only provided that the market is risk-neutral. Over and above these conclusions relating to options, the study also deals with the problem of valuing warrants. It is shown that under simple preconditions warrants can be formally treated as call options after allowing for their watering effect. Under the same assumptions, it proves that the issue of warrants has no effect on the market value of the issuing firm - a special variant of the Modigliani-Miller theorem on the invariance of capital costs relative to capital structure changes.