Much effort has gone into the study of financial markets and how prices vary with time.
Charles DowCharles Henry Dow was an American journalist who co-founded Dow Jones & Company with Edward Jones and Charles Bergstresser....
, one of the founders of
Dow Jones & CompanyDow Jones & Company is an American publishing and financial information firm.The company was founded in 1882 by three reporters: Charles Dow, Edward Jones, and Charles Bergstresser. Like The New York Times and the Washington Post, the company was in recent years publicly traded but privately...
and
The Wall Street JournalThe Wall Street Journal is an English-language international daily newspaper published by Dow Jones & Company, a division of News Corporation, in New York City, with Asian and European editions. As of 2007, it has a worldwide daily circulation of more than 2 million, with approximately 931,000...
, enunciated a set of ideas on the subject which are now called
Dow TheoryDow Theory is a heterodox theory on stock price movements that includes what is now called technical analysis as well as some portion of sector rotation. The theory was derived from 255 Wall Street Journal editorials written by Charles H. Dow , journalist, founder and first editor of the Wall...
. This is the basis of the so-called
technical analysisTechnical analysis is a security analysis discipline for forecasting the future direction of prices through the study of past market data, primarily price and volume.-History:...
method of attempting to predict future changes. One of the tenets of "technical analysis" is that
market trendsA market trend is a putative prevailing course or tendency of a financial market to move in a particular direction over time. These trends are classified as secular trends , primary trends and secondary trends...
give an indication of the future, at least in the short term. The claims of the technical analysts are disputed by many academics, who claim that the evidence points rather to the
random walk hypothesisThe random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the prices of the stock market cannot be predicted. It has been described as 'jibing' with the efficient market hypothesis. Economists have historically accepted the random...
, which states that the next change is not correlated to the last change.
The scale of changes in price over some unit of time is called the
volatilityVolatility most frequently refers to the standard deviation of the continuously compounded returns of a financial instrument with a specific time horizon. It is often used to quantify the risk of the instrument over that time period. Volatility is typically expressed in annualized terms, and it...
.
Much effort has gone into the study of financial markets and how prices vary with time.
Charles DowCharles Henry Dow was an American journalist who co-founded Dow Jones & Company with Edward Jones and Charles Bergstresser....
, one of the founders of
Dow Jones & CompanyDow Jones & Company is an American publishing and financial information firm.The company was founded in 1882 by three reporters: Charles Dow, Edward Jones, and Charles Bergstresser. Like The New York Times and the Washington Post, the company was in recent years publicly traded but privately...
and
The Wall Street JournalThe Wall Street Journal is an English-language international daily newspaper published by Dow Jones & Company, a division of News Corporation, in New York City, with Asian and European editions. As of 2007, it has a worldwide daily circulation of more than 2 million, with approximately 931,000...
, enunciated a set of ideas on the subject which are now called
Dow TheoryDow Theory is a heterodox theory on stock price movements that includes what is now called technical analysis as well as some portion of sector rotation. The theory was derived from 255 Wall Street Journal editorials written by Charles H. Dow , journalist, founder and first editor of the Wall...
. This is the basis of the so-called
technical analysisTechnical analysis is a security analysis discipline for forecasting the future direction of prices through the study of past market data, primarily price and volume.-History:...
method of attempting to predict future changes. One of the tenets of "technical analysis" is that
market trendsA market trend is a putative prevailing course or tendency of a financial market to move in a particular direction over time. These trends are classified as secular trends , primary trends and secondary trends...
give an indication of the future, at least in the short term. The claims of the technical analysts are disputed by many academics, who claim that the evidence points rather to the
random walk hypothesisThe random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the prices of the stock market cannot be predicted. It has been described as 'jibing' with the efficient market hypothesis. Economists have historically accepted the random...
, which states that the next change is not correlated to the last change.
The scale of changes in price over some unit of time is called the
volatilityVolatility most frequently refers to the standard deviation of the continuously compounded returns of a financial instrument with a specific time horizon. It is often used to quantify the risk of the instrument over that time period. Volatility is typically expressed in annualized terms, and it...
. In 1900,
Louis BachelierLouis Jean-Baptiste Alphonse Bachelier was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, .His thesis, which discussed the...
modeled the
time seriesIn statistics, signal processing, and many other fields, a time series is a sequence of data points, measured typically at successive times, spaced at time intervals...
of changes in the
logarithmIn mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number....
of stock prices as a
random walkA random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. The results of random walk analysis have been applied to computer science, physics, ecology, economics, and a number of other fields as a fundamental model for...
in which the short-term changes had a finite
varianceIn probability theory and statistics, the variance of a random variable or distribution is the expected square deviation of that variable from its expected value or mean, or to put it another way: variance is the measure of the amount of variation of all the scores for a variable...
. This causes longer-term changes to follow a Gaussian distribution.
Modeling the changes by distributions with finite variance is now known to be inappropriate. In the 1960s it was discovered by
Benoît MandelbrotBenoît B. Mandelbrot is a French American mathematician, best known as the father of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University; IBM Fellow Emeritus at the Thomas J. Watson Research Center; and Battelle Fellow at the Pacific Northwest National...
that changes in prices do not follow a Gaussian distribution, but are rather modeled better by Lévy stable distributions. The scale of change, or volatility, depends on the length of the time interval to a
powerA power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, and the other is the size of the event, then the relationship has a power-law distribution when the frequency of the event decreases at a greater rate than the size...
a bit more than 1/2. Large changes up or down are more likely than what one would calculate using a Gaussian distribution with an estimated
standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
.
See also
- Black-Scholes model
- Econometrics
Econometrics is concerned with the tasks of developing and applying quantitative or statistical methods to the study and elucidation of economic principles. Econometrics combines economic theory with statistics to analyze and test economic relationships...
- Engle, Robert F.
Robert Fry Engle III is an American economist and the winner of the 2003 Nobel Memorial Prize in Economic Sciences, sharing the award with Clive Granger, "for methods of analyzing economic time series with time-varying volatility ".-Biography:Engle was born in Syracuse, New York and went on to...
- GARCH
- Generalized hyperbolic distribution
- Granger, Clive
Sir Clive William John Granger was a British economist, and Professor Emeritus at the University of California, San Diego. In 2003, Granger was awarded the Nobel Memorial Prize in Economic Sciences. In bestowing this honor, the Royal Swedish Academy of Sciences committee recognized that Granger...
- Itō's lemma
In mathematics, Itō's lemma is used in Itō stochastic calculus to find the differential of a function of a particular type of stochastic process. It is the stochastic calculus counterpart of the chain rule in ordinary calculus and is best memorized using the Taylor series expansion and retaining...
- Lévy process
In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is any continuous-time stochastic process that starts at 0, admits càdlàg modification and has "stationary independent increments" — this phrase will be explained below...
- Mathematical finance
Mathematical finance comprises the branches of applied mathematics concerned with the financial markets.The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive, and extend,...
- Pearson distribution
The Pearson distribution is a family of continuous probability distributions. It was first published by Karl Pearson in 1895 and subsequently extended by him in 1901 and 1916 in a series of articles on biostatistics.- History :...
s
- Realized volatility
- Risk modeling
Risk modeling refers to the use of formal econometric techniques to determine the aggregate risk in a financial portfolio. Risk modeling is one of many subtasks within the broader area of financial modeling....
- Stochastic volatility
Stochastic volatility models are used in the field of quantitative finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the...
- Wiener process
In mathematics, the Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It is often called Brownian motion, after Robert Brown...
External links