Clifford A. Ball

A Simplified Jump Process for Common Stock Returns

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.

Stochastic Volatility Option Pricing

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.

The Decision to Establish a Foreign Bank Branch or Subsidiary: An Application of Binary Classification Procedures

This paper has two purposes. First, we model a key decision for international banks using data on the foreign direct investment (FDI) behavior of foreign banks in Japan and California. Second, we examine the utility of linear discriminant analysis and maximum likelihood logit analysis as statistical techniques for relating a qualitative dependent variable to a vector of independent variables.

The stochastic volatility of short-term interest rates: Some international evidence

This paper estimates a stochastic volatility model of short-term riskless interest rate dynamics. Estimated interest rate dynamics are broadly similar across a number of countries and reliable evidence of stochastic volatility is found throughout. In contrast to stock returns, interest rate volatility exhibits faster mean-reverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility reflects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news. Copyright The American Finance Association 1999.

The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing

the market requires efficient estimation of the Assuming security price dynamics are governed by a diffusion process and given the publicly most available form of data, this paper provides the maximum likelihood estimator of security price volatility. A Monte Carlo simulation compares the small-sample properties of this and other proposed security price volatility estimators. The resultant maximum likelihood estimator of the Black-Scholes call option price formulation is also derived. For small sample sizes a Monte Carlo simulation study facilitates comparison with other proposed estimation procedures. Also, the statistically most powerful confidence intervals for the BlackScholes call option price are constructed. * We would like to thank the participants of the Statistics Department Seminar and Finance Department Workshop at the University of Michigan for their helpful comments. We are especially grateful to Fred Hoppe, Adrian Tschoegl, and an anonymous referee for their insightful suggestions. Any remaining errors are our responsibility.

Unit roots and the estimation of interest rate dynamics

This paper investigates the time series estimation of Cox, Ingersoll, and Rosss square root, mean-reverting specification for interest rate dynamics. For a priori resonable mean reversion, the stochastic behavior of interest rates is sufficiently close to a non-stationary process with a unit root so that least squares, the generalized method of moments, as well as maximum likelihood estimation provide upward biased estimates of the models speed of adjustment coefficient. Corresponding bond yields, as a result, exhibit excessive mean reversion. In addition, estimates of the specifications long-term mean interest rate are seen to display erratic behavior when near a unit root. These conclusions are robust to assuming multiple state variable specifications, such as Brennan and Schwartzs two factor model of interest rate dynamics. We also document conditions under which this unit root problem can be alleviated when the cross-sectional restrictions of the Cox, Ingersoll, and Ross single factor term structure model are imposed.

Bond Price Dynamics and Options

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.

Investigating security-price performance in the presence of event-date uncertainty

Abstract This paper introduces an event-study method that incorporates the possibility of a random event date. Consistent with empirical evidence, we assume an event may affect not only the conditional mean of a securitys return, but also its conditional variance. We compare the statistical power and efficiency of our maximum-likelihood method with the standard application of traditional event-study methods to multiday security returns. Assuming a two-day event period, our empirical results provide evidence that the multiday approach is robust. We use our maximum-likelihood method to investigate the valuation effects of stock splits and stock dividends.

A jump diffusion model for the European monetary system

Abstract We propose a general continuous time bivariate jump-diffusion representation for the exchange rates of European currencies. Our model captures key features of the exchange rate mechanism. Fluctuation within bilateral limits is modeled by appropriate diffusion dynamics, while discontinuous variation in the level of the fluctuation band is posited to have a jump structure. Under specific assumptions, the probability distribution of the exchange rate process is derived analytically. We also perform an empirical investigation of these exchange rates. Comparing the fit of alternative models, we find some evidence of mean reversion inside the bands for these exchange rates. (JEL F33, C51).

A Nonparametric Approach to Accelerated Life Testing

Abstract A nonparametric model of acceleration is introduced. Based on this model, a procedure is suggested for estimating the nonaccelerated life distribution from accelerated observations. Unlike previous nonparametric estimation procedures, our method does not require nonaccelerated observations. A relationship between the accelerated and the nonaccelerated distributions is assumed but there is variety in that choice. A comparison of our method with the power rule method under the assumption of exponential lifetimes reveals that in some instances our method is asymptotically equivalent to the maximum likelihood method for estimating the nonaccelerated mean lifetime. Simulation for small sample sizes completes the comparison.