In econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.
Robert Fry Engle III is an American economist and statistician. He won 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 (ARCH)".
In social sciences, especially economics, a stylized fact is a simplified presentation of an empirical finding. Stylized facts are broad tendencies that aim to summarize the data, offering essential truths while ignoring individual details.
Financial econometrics is the application of statistical methods to financial market data. Financial econometrics is a branch of financial economics, in the field of economics. Areas of study include capital markets, financial institutions, corporate finance and corporate governance. Topics often revolve around asset valuation of individual stocks, bonds, derivatives, currencies and other financial instruments.
Financial modeling is the task of building an abstract representation of a real world financial situation. This is a mathematical model designed to represent the performance of a financial asset or portfolio of a business, project, or any other investment.
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed. Different research communities favor one or the other largely for historical reasons, and may have differences in the precise definition of either.
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical 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 underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others.
Ole Eiler Barndorff-Nielsen was a Danish statistician who has contributed to many areas of statistical science.
In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations that have a tendency to occasionally be much farther from the average than is expected for a normal distribution.
Tim Peter Bollerslev is a Danish economist, currently the Juanita and Clifton Kreps Professor of Economics at Duke University. A fellow of the Econometric Society, Bollerslev is known for his ideas for measuring and forecasting financial market volatility and for the GARCH model.
Neil Shephard, FBA, is an econometrician, currently Frank B. Baird Jr., Professor of Science in the Department of Economics and the Department of Statistics at Harvard University.
In finance, volatility is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns.
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial time series typically assume homoskedasticity and normality cannot explain stylized phenomena such as skewness, heavy tails, and volatility clustering of the empirical asset returns in finance. In 1963, Benoit Mandelbrot first used the stable distribution to model the empirical distributions which have the skewness and heavy-tail property. Since -stable distributions have infinite -th moments for all , the tempered stable processes have been proposed for overcoming this limitation of the stable distribution.
Bruno Dupire is a researcher and lecturer in quantitative finance. He is currently Head of Quantitative Research at Bloomberg LP. He is best known for his contributions to local volatility modeling and Functional Itô Calculus. He is also an Instructor at New York University since 2005, in the Courant Master of Science Program in Mathematics in Finance.
In financial econometrics, the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fisher that incorporates stochastic volatility components of heterogeneous durations. MSM captures the outliers, log-memory-like volatility persistence and power variation of financial returns. In currency and equity series, MSM compares favorably with standard volatility models such as GARCH(1,1) and FIGARCH both in- and out-of-sample. MSM is used by practitioners in the financial industry to forecast volatility, compute value-at-risk, and price derivatives.
Realized variance or realised variance is the sum of squared returns. For instance the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month. More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day.
Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include derivative structuring or pricing, risk management, investment management and other related finance occupations. The occupation is similar to those in industrial mathematics in other industries. The process usually consists of searching vast databases for patterns, such as correlations among liquid assets or price-movement patterns.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
Stephen John Taylor is an emeritus professor of Finance at Lancaster University Management School, an authority on stochastic volatility models and option prices, a researcher in the areas of financial econometrics and mathematical finance, and an author who has published academic books and influential learned papers in Mathematical Finance, the Journal of Financial and Quantitative Analysis, the Journal of Econometrics and several other academic journals
Rama Cont is the Professor of Mathematical Finance at the University of Oxford. He is known for contributions to probability theory, stochastic analysis and mathematical modelling in finance, in particular mathematical models of systemic risk. He was awarded the Louis Bachelier Prize by the French Academy of Sciences in 2010.
