Executive compensation, Executive stock options, Equilibrium warrant pricing model, APB opinion No. 25

In this paper we confront two well-known models for pricing options. It shows how the two models, one derived in a discrete time framework by Boness, the other derived in a continuous time framework by Black and Scholes, can be made consistent. In doing so, we find the implicit, discrete period, discount factor for the call option. Several characteristics of the discount factor are analyzed and compared to the characteristics of the instantaneous expected rate of return on the call.

In this paper the lower boundary conditions for traded options are derived and subjected to empirical testing. Two hypotheses are formulated based on the theoretical conditions and tested on data on call options traded on the Chicago Board Options Exchange. The first hypothesis argues that the stock and options markets are well synchronized so that simultaneous closing prices are within the theoretical boundaries. The evidence in the ex post test is inconsistent with this hypothesis. The second hypothesis claims the markets to be efficient. The tests are directed toward the question whether arbitrage profits could actually have been made on the Exchange by exploiting the violations of the dominance condition. The tests, carried out as ex ante tests, indicate that positive profits could have been exploited on the average, but the magnitude of the average was small relative to the dispersion of the yields.

According to the current state of knowledge in finance, the expected rate of return adjusted for risk is independent of the stock price. The basic proposition of the capital asset pricing model (CAPM) is that the expected rate of return for each security is a function of the “risk” of that security, and that this risk is measured by the contribution of the security to the variability of the market portfolio. The implication of the CAPM is that knowing the price of a security perse will add nothing to predicting its expected rate of return.