On Arbitrage, Information Costs, Compound Options and the Valuation of the Firm and Its Assets

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.