Title: On Arbitrage, Information Costs, Compound Options and the Valuation of the Firm and Its Assets
Abstract: ABSTRACT This paper presents a simple framework for the valuation of compound options within a context of incomplete information. Information costs are linked to the theory of signaling, agency models and generic stocks in the spirit of Merton's (1987) model of capital market equilibrium with incomplete information. We propose some ideas to explain arbitrage in financial markets in the presence of information costs. The use of these costs is important in the valuation of equity of some firms in the new economy like Internet stocks. Equity in these firms cannot be valued in an appropriate way by a model ignoring information uncertainty. When deriving the compound call option formula, we consider a call option on a stock, which is itself an option on the assets of the firm. Our methodology incorporates shadow costs of incomplete information on the firm's assets as well as the effects of leverage in the capital structure. The compound option formula is derived using two approaches: the standard Black and Scholes approach and the martingale method. The formula can be useful in the valuation of several corporate liabilities in the presence of information uncertainty about the firm and its cash flows. Our analysis can be used for the valuation of several real options. JEL: G3, G31, G32, G33 Keywords: Options; Arbitrage; Pricing; Information costs I. INTRODUCTION The compound option or an option on an option has been studied in a context of complete information by several authors including Black and Scholes (1973), Geske (1979), Triantis and Hodder (1990), Briys-Bellalah et al. (1998), etc. The concept of an option on an option is important in the study of several opportunities with a sequential nature where some of them are available only if earlier opportunities are undertaken. For a survey of this literature on real standard and complex options, the reader can refer to Dixit and Pindyck (1994), Triantis and Hodder (1990) and Grenadier and Weiss (1997) among others. Black and Scholes (1973), Black and Cox (1976), Galai and Masulis (1976) and Geske (1979) show that several corporate liabilities may be considered as options. In a context of complete information, they study the pricing of a firm's common stock and bonds by considering the stock as an option on the firm's value. They show that corporate investment opportunities may be analyzed as options and compound options. However, their analysis does not account for information uncertainty. Since the acquisition of information and its dissimination are central activities in finance, and especially in capital markets, Merton (1987) develops a model of capital market equilibrium with incomplete information, CAPMI, to provide some insights into the behavior of security prices. He also studies the equilibrium structure of asset prices and its connection with empirical anomalies in financial markets. In this spirit, Bellalah (1990) and (1999) provides a valuation formula for stock options and commodity options in a context of incomplete information. The formula is derived in an equilibrium approach by a simple extension of the main results in Merton's model. In this paper, we use arbitrage arguments rather than an equilibrium approach to derive the formula in a Black and Scholes (1973) economy. Such a formula might be applied to the valuation of equity in the capital structure of the firm. The use of information costs regarding the firm and its cash flows might help to understand why Black and Scholes model leads to theoretical prices, which are systematically biased. The information uncertainty about the firm and its cash flows reflects the agency costs and the asymmetric information problems. By assuming the stock as an option on the value of the firm, the value of the call as a compound option can be derived as a function of the firm's value by accounting for information costs and the effects of leverage. …
Publication Year: 2003
Publication Date: 2003-09-22
Language: en
Type: article
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