Knowledge that Transforms

Black and Scholes [1] derived the pricing equation for a European put when the stock price follows geometric Brownian motion. For this same case, Merton [5] derived the pricing equation for an American put with infinite time to maturity. Brennan and Schwartz [2], Rubinstein and Cox [7], and Parkinson [6] have developed numerical solutions for the price of an American put. Numerical solutions are expensive and do not provide much intuition. Naturally, an analytic solution would be much preferred; unfortunately, pricing the American put requires solving a formidable and presumably intractable boundary value problem.

Merger transactions involve differing degrees of change in capital structure and asset distribution. As a result, different forms of merger could have different effects on security values of the firms involved. Previous empirical studies primarily used samples that included all types of mergers. The present study examines the effect of one type of merger, pure stock exchange, on the values of the debt and equity of the firms involved.

Robert M. Bowen, Richard P. Castanias, Lane A. Daley, Intra-Industry Effects of the Accident at Three Mile Island, The Journal of Financial and Quantitative Analysis, Vol. 18, No. 1 (Mar., 1983), pp. 87-111

The specification of a statistical distribution which accurately models the behavior of stock returns continues to be a salient issue in financial economics. With the introduction of arithmetic and geometric Brownian motion models, much attention has recently focused on a Poisson mixture of distributions as an appropriate specification of stock returns. For example, see [12], [3], [8], [10], [5], and [1]. Consistent with empirical evidence, these models yield leptokurtic security return distributions and, furthermore, the specification has much economic intuition. In particular, one may always decompose the total change in stock price into “normal” and “abnormal” components. The “normal” change may be due to variation in capitalization rates, a temporary imbalance between supply and demand, or the receipt of any other information which causes marginal price changes. This component is modelled as a lognormal diffusion process. The “abnormal” change is due to the receipt of any information which causes a more than marginal change in the price of the stock and is usually modeled as a Poisson process.