Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test1988
In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at difference frequencies. The random walk model is strongly rejected for the entire sample period (1962-1985) and for all subperiods for a variety of aggregate returns indexes and size-sorted portfolios. Although the rejections are due largely to behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or time-varying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.
Semiparametric Upper Bounds for Option Prices and Expected Payoffs1987
Upper bounds on the expected payoff of call and put options are derived. These bounds depend only on the mean and variance of the terminal stock price and not on its entire distribution, so they are termed semi-parametric. A corollary of this result is a set of upper bounds for option prices obtained by the risk-neutral valuation approach of Cox and Ross. As an example, these bounds are shown to obtain across both lognormal diffusion-jump processes for any given data set. We present an illustrative example that suggests these bounds may be of considerable practical value.
Statistical Tests of Contingent-Claims Asset-Pricing Models: A New Methodology1986
A new methodology for statistically testing contingent-claims asset-pricing models based on asymptotic statistical theory is proposed. It is introduced in the context of the Black-Scholes option-pricing model, for which some illustrative estimation, inference, and simulation results are also presented. The proposed methodology is then extended to arbitrary contingent claims by first considering the estimation problem for general Itô processes and then deriving the asymptotic distribution of a general contingent claim which depends upon such Itô processes.
Logit Versus Discriminant Analysis: A Specification Test with Applications to Corporate Bankruptcies1986
Two of the most widely used statistical techniques for analyzing discrete economic phenomena are discriminant analysis (DA) and logit analysis. For purposes of parameter estimation, logit has been shown to be more robust than DA. However, under certain distributional assumptions both procedures yield consistent estimates and the DA estimator is asympototically efficient. This suggests a natural Hausman specification test of these distributional assumptions by comparing the two estimators. In this paper, such a test is proposed and an empirical example involving corporate bankruptcies is provided. The finite-sample properties of the test statistic are also explored through some sampling experiments.
A Large-Sample Chow Test for the Single Linear Simultaneous Equation1985
The practice of risk management starts with an understanding of the statistical behavior of financial asset prices over time. Models such as the random walk hypothesis, the martingale model, and geometric Brownian motion are fundamental to any analysis of financial risks and rewards, particularly for longer investment horizons. Recent empirical evidence has cast doubt on some of these models, and this article provides an overview of such evidence. I begin with a review of the random walk hypothesis and related models, including a discussion of why such models perform so poorly, and then turn to some current research on alternative models such as long-term memory models and stable distributions.