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.

This paper provides a closed-form, preference-free means of valuing a European call option written on a default-free pure discount bond. Investors may not agree upon a theory of the term structure, but they will necessarily agree on equilibrium option values. Further, these equilibrium option values may be obtained without recourse to numerical approximation.Default-free pure discount bond prices were posited to follow a non-standardized transformed Brownian bridge process. This specification implicitly incorporates the terminal constraint that the price of a default-free pure discount bond equal its face value at maturity.Contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities. The Brownian bridge specification permits an appropriate means of incorporating a number of such constraints. Therefore, while this paper has considered only the application of the Brownian bridge process to the valuation of debt options, the introduction of this process may provide for many further financial applications.

Clifford A. Ball, Adrian E. Tschoegl, The Decision to Establish a Foreign Bank Branch or Subsidiary: An Application of Binary Classification Procedures, The Journal of Financial and Quantitative Analysis, Vol. 17, No. 3 (Sep., 1982), pp. 411-424

This paper examines alternative methods for pricing options when the underlying security volatility is stochastic. We show that when there is no correlation between innovations in security price and volatility, the characteristic function of the average variance of the price process plays a pivotal role. It may be used to simplify Fourier option pricing techniques and to implement simple power series methods. We compare these methods for the alternative mean-reverting stochastic volatility models introduced by Stein and Stein (1991) and Heston (1993). We also examine the biases in the Black-Scholes model that are eliminated by allowing for stochastic volatility, and we correct some errors in the Stein and Stein (1991) analysis of this issue.