Stock Price Distribution Research Articles

The weekend effect on the distribution of stock prices

Abstract Evidence of weekend effects on the distribution of security returns suggests that returns are generated by a process operating closer to trading time rather than calendar time. In contrast, accumulation of interest over the weekend follows a calendar-time process. Since both the variance of returns and the interest rate are important parameters of the Black-Scholes option pricing model, this paper suggests that the model be stated to account for this by utilizing a trading-time variance and a calendar-time interest rate. Empirical evidence indicates that this allows the model to better explain market option prices.

Option Pricing Bounds in Discrete Time

ABSTRACTUpper and lower bounds are derived for call options traded at discrete intervals. These bounds are independent of assumptions on the stock price distribution other than a restriction satisfied by the stock being “non‐negative beta.” The development of the bounds relies on the single‐price law and arbitrage arguments. Both single‐period and multiperiod results are produced, and put option bounds follow by extension. The bounds exist as equilibrium values given a consensus on stock price distribution; they are also valid for empirical studies, being adjustable for dividends and commissions.

Stable Distributions and the Mixtures of Distributions Hypotheses for Common Stock Returns

Abstract The form of the distribution underlying common stock returns has many implications for financial modeling. Among the frequently proposed models for stock return distributions is the family of stable distributions. Numerous studies of stock return distributions have also proposed various types of mixtures of normal distributions. This article examines the characteristics of several different combinations of mixtures of normal and stable distributions, and compares them with actual stock price distributions. The principal tests applied are based on the stability-under-addition property of stable distributions.

Stable Distributions and the Mixtures of Distributions Hypotheses for Common Stock Returns

Abstract The form of the distribution underlying common stock returns has many implications for financial modeling. Among the frequently proposed models for stock return distributions is the family of stable distributions. Numerous studies of stock return distributions have also proposed various types of mixtures of normal distributions. This article examines the characteristics of several different combinations of mixtures of normal and stable distributions, and compares them with actual stock price distributions. The principal tests applied are based on the stability-under-addition property of stable distributions.

Macroinformation and the Variability of Stock Market Prices

A POPULAR TOPIC FOR empirical research in financial markets has been the distribution of stock market prices. The most widely accepted finding is that security price changes in securities markets tend to be intertemporally independent, that is, that securities markets are weak-form efficient as that term is used by Fama (1970) and others.'2 A second hypothesis, apparently widely held, is that a stock's price changes in efficient markets will be drawn from a fixed, stationary distribution. This second hypothesis is implicitly or explicitly assumed in most empirical applications involving the Capital Asset Pricing Model, and in most studies of stock price distributions based upon ARIMA models, spectral analysis, or any specific distribution such as the normal, t, or infinite variance stable paretian distributions. However, the stationary distribution hypothesis is neither an implication of intertemporal independence of price changes nor borne out independently by other empirical evidence. This paper is concerned with the hypothesis that efficient markets and random changes in the public information set jointly will tend to generate observed distributions of price changes which will not generally be characterized by the simple distributions frequently discussed in the literature. In particular, we argue that the variability of the daily market factor is an increasing function of the rate of arrival of information of broad economic impact. We also are interested in ascertaining whether markets in an aggregate sense are efficient processors of macroinformation. In the next section we briefly review previous work and discuss the time series used here to proxy the market factor. The empirical behavior of the market factor is similar to that of most highly traded assets; that is, the empirical distribution is fat-tailed, weakly autocorrelated and nearly symmetric. Another interesting finding is that there is substantial variation in the variability of the daily market factor during the 1973-1977 period. We then observe that the empirical distribution of the market factor resembles an information driven subordinated stochastic process. This is equivalent to saying that the variance of the process governing the behavior is itself stochastic, and that it is the arrival of new macroinformation which to a great extent determines the changing variability of the market factor. The fluctuating variability of the market factor, in turn, can * University of Washington. ' Lucas (1978) has developed a model of security prices in a pure exchange economy which identifies a set of sufficient conditions for the Martingale property to obtain. 2 It is frequently argued that efficiency implies rational expectations and competitive (but not the converse), given assumptions sufficient for the equilibrium to exist.

Option Pricing: The American Put

The problem of correctly, or perhaps rationally, setting the price of an option on a stock has been attacked many times.' Recently, Black and Scholes developed a very neat argument which provided a solution for the so-called European put and call options, and thus indirectly for the American call option.2 For it can be shown that it is better to retain an American call option until expiration rather than to convert it before expiration.3 In their paper, Black and Scholes also indicated that no formula for the value of an American put option had been constructed as yet. In Section IV of this paper, we present such a formula for the value of an American put option. In order to justify it, in Section II we review and discuss our assumptions about stock prices and their probability distributions. In Section III, we review and discuss the idea of a free and efficient options market and its consequences. In Section IV, we write down a general formula for American put and call options, and then assume for the first time in the paper that the distribution of stock prices is approximately lognormal, thus obtaining an explicit formula for the American put option. A graph of the predictions for a put option is presented; a table of put values is given which is suitable for most applications; and a limited comparison is made between the derived put formula and empirical data. The agreement is as good as can be expected, given the data available. In Section V, there are a summary and conclusions.