Financial Econometric Theory

Financial Econometric Theory

Ideally mathematical or statistical models could predict the behavior of economic and financial phenomena such as market fluctuations. For example, option prices can be calculated using fast Fourier Transform (FFT). Some of the most commonly encountered theoretical concepts in econometric research are outlined below.

Random Walk, ARCH & GARCH. The Random Walk Hypothesis refers to the stochastic (random, non-deterministic) behavior of stock, where no point can be predicted. The scenario is changed with the autoregressive conditional heteroskedasticity (ARCH) model, and its generalized substitute, GARCH. Both concepts account for volatility.

White’s test of heteroskedasticity elucidates the position of residual variance of a variable in a regression model; if the position is constant it is called homoscedasticity. The GARCH model can be used once homoscedasticity is ruled out.

Skedastic function is of interest to mesoeconomists. Mesoeconomics is a new and debated arrival, reserved for items that fail to be easily categorized as pertaining to macro- or microeconomics.

Black Sholes Model. The item would be impossible to explain without mentioning the continuous hedging argument, Girsanov’s Theorem pricing kernel, one-factor Cox-Ingersoll-Ross (CIR) model interest rates, and others, which would fall outside desired conciseness limits. The Black Sholes formula is illustrious. A corresponding option calculator, similar to a mortgage calculator, is easily found online.

It's nice to take a nap after many hours spent in learning the financial economeetric theory. Photo by Elena

Levy Processes. Geometric Brownian motion is a Levy process that was initially intended as a stock price model (Engle, 2001). Levy processes are computational tools to determine price dynamics. Raible (1998) shows exponential Levy process modeling stock price. In the Levy term structure model, term structure refers to the relationship between a bond’s maturity date and the interest rate.

Method-of-Moment. Generalized Methods-of-Moment (GMM) is a reliable method-of-moment based parameters estimation procedure. Maximum Likelihood Estimation (MLE), Quasi-Maximum Likelihood Estimator (QMLE), Efficient Methods-of-Moment (EMM) in addition to Bayesian and adaptive, are all estimation procedures.

CAPM. The Capital-Asset Pricing Model (CAPM) appears eminently in the accounting and financial industries. The CAPM abbreviation is sometimes confused with the Certified Associate in Project Management (also CAPM) certification.

MCMC. Markov Chain Monte Carlo (MCMC) simulation; Markov process. Andrey Markov was a Russian mathematician in the late 1800s – early 1900s. The Monte Carlo method was named after the celebrated Monte Carlo casino. The integration method and study are used to calculate continuous time asset pricing models, to cite an illustration.

Clifford-Hammersley or Hammersley-Clifford theorem, has nearly stole the show as far as financial estimations and predictions go. Authors with reflective names derived the theorem based on the positivity condition. The use is widespread: graphical, spatial models, MCMC, point processes, spatial statistics such as quantitative geography and topographical analysis.

Distributions and methods can be paparametric, semiparametric as well as nonparametric, characteristic criteria apply. Hong & Nekipelov (2010) derive the semiparametric efficiency bound under the monotonicity assumption. The article is rendered available by the open access journal Quantitative Economics and The Econometric Society.

Lastly, seriation plays an important role in statistical analysis. In finance, financial time series often come in handy in elucidating behavior of the stock market over several decades.

References:

    Engle, R. (2001). Financial econometrics – A new discipline with new methods. Journal of Econometrics, 100 (1): 53-56.

    Geweke, J. & Zhou, G. (1996). Measuring the pricing error of the arbitrage pricing theory. The Review of Financial Studies, 9 (2): 557-587.

    Hong, H. & Nekipelov, D. (2010). Semiparametric efficiency in nonleanar LATE models. Quantitative Economics, 1: 279-304.

    Raible, S. (1998). Levy processes in finance: Theory, numerics, and empirical facts. PhD Thesis. Mathematics Faculty, Freiburg University, Freiburg.