Financial econometrics

Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital.

Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". The first known use of the term "econometrics" was by Polish economist Paweł Ciompa in 1910. Jan Tinbergen is considered by many to be one of the founding fathers of econometrics. Ragnar Frisch is credited with coining the term in the sense in which it is used today.

Investment management is the professional asset management of various securities and other assets in order to meet specified investment goals for the benefit of the investors. Investors may be institutions or private investors.

In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line. The theory was proposed by the economist Stephen Ross in 1976. The linear factor model structure of the APT is used as the basis for many of the commercial risk systems employed by asset managers.

Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the variance of asset prices as a proxy for risk.

Cointegration is a statistical property of a collection (X₁, X₂, ..., X_k) of time series variables. First, all of the series must be integrated of order d. Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that aX + bY + cZ is integrated of order less than d, then X, Y, and Z are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trends—either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series have stochastic trends—these are also called unit root processes, or processes integrated of order . They also showed that unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them.

Eric Ghysels is a Belgian economist with particular interest in finance and time series econometrics who works in the field of financial econometrics, and is currently the Edward M. Bernstein Distinguished Professor of Economics at the University of North Carolina and a Professor of Finance at the Kenan-Flagler Business School.

Econometrica is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. The current editor-in-chief is Joel Sobel.

The Journal of Econometrics is a scholarly journal in econometrics. It was first published in 1973. Its current editors are A. Ronald Gallant, John Geweke, Cheng Hsiao, and Peter M. Robinson.

The Journal of Business & Economic Statistics is a quarterly peer-reviewed academic journal published by the American Statistical Association. The journal covers a broad range of applied problems in business and economic statistics, including forecasting, seasonal adjustment, applied demand and cost analysis, applied econometric modeling, empirical finance, analysis of survey and longitudinal data related to business and economic problems, the impact of discrimination on wages and productivity, the returns to education and training, the effects of unionization, and applications of stochastic control theory to business and economic problems.

Real options valuation, also often termed real options analysis, applies option valuation techniques to capital budgeting decisions. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real call or put option, respectively.

A quantitative analyst is a person who specializes in the application of mathematical and statistical methods to financial and risk management problems. The occupation is similar to those in industrial mathematics in other industries.

In finance, volatility clustering refers to the observation, first noted as Mandelbrot (1963), that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes." A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|r_t|, |r_t+τ |) > 0 for τ ranging from a few minutes to several weeks. This empirical property has been documented in the 90's by Granger and Ding (1993) and Ding and Granger (1996) among others; see also. Some studies point further to long-range dependence in volatility time series, see Ding, Granger and Engle (1993) and Barndorff-Nielsen and Shephard.

In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.

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.

Kenneth Jan Singleton is an American economist. He is a leading figure in empirical financial economics, and a faculty member at Stanford University.

The following outline is provided as an overview of and topical guide to finance:

Statistical finance, is the application of econophysics to financial markets. Instead of the normative roots of much of the field of finance, it uses a positivist framework including exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets. The starting point for this approach to understanding financial markets are the empirically observed stylized facts.

A master's degree in Financial Economics provides a rigorous understanding of theoretical finance and the economic framework upon which that theory is based. The degree is postgraduate, and usually incorporates a thesis or research component. Programs may be offered jointly by the business school and the economics department.

Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock. The fundamental theorem of arbitrage-free pricing is one of the key theorems in mathematical finance, while the Black–Scholes equation and formula are amongst the key results.

Campbell Russell "Cam" Harvey is a Canadian economist, known for his work on asset allocation with changing risk and risk premiums and the problem of separating luck from skill in investment management. He is currently the J. Paul Sticht Professor of International Business at Duke University's Fuqua School of Business in Durham, North Carolina, as well as a research associate with the National Bureau of Economic Research in Cambridge, Massachusetts. He is also a research associate with the Institute of International Integration Studies at Trinity College in Dublin and a visiting researcher at University of Oxford. He served as the 2016 president of the American Finance Association.

Stephen John Taylor is a semi-retired British 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

Francis X. Diebold is an American economist known for his work in predictive econometric modeling, financial econometrics, and macroeconometrics. He earned both his B.S. and Ph.D. degrees at the University of Pennsylvania ("Penn"), where his doctoral committee included Marc Nerlove, Lawrence Klein, and Peter Pauly. He has spent most of his career at Penn, where he has mentored approximately 75 Ph.D. students. Presently he is Paul F. and Warren S. Miller Professor of Social Sciences and Professor of Economics at Penn’s School of Arts and Sciences, and Professor of Finance and Professor of Statistics at Penn’s Wharton School. He is also a Faculty Research Associate at the National Bureau of Economic Research in Cambridge, Massachusetts, and author of the No Hesitations blog.

High frequency data refers to time-series data collected at an extremely fine scale. As a result of advanced computational power in recent decades, high frequency data can be accurately collected at an efficient rate for analysis. Largely used in financial analysis and in high frequency trading, high frequency data provides intraday observations that can be used to understand market behaviors, dynamics, and micro-structures.